Publications – Dynamical Systems at Imperial College London (DynamIC)

Konstantinos Kourliouros, Jeroen S. W. Lamb, Martin Rasmussen, Wei Hao Tey, Kalle G. Timperi, and Dmitry Turaev, Persistence of minimal invariant sets for certain set-valued dynamical systems: a boundary mapping approach. DynamIC Preprint 2023-1
Flavia Remo, Gabriel Fuhrmann, and Tobias Jäger, On the effect of forcing of fold bifurcations and early-warning signals in population dynamics. DynamIC Preprint 2019-6
Thai Son Doan, Jeroen S.W. Lamb, Julian Newman, and Martin Rasmussen, Classification of random circle homeomorphisms up to topological conjugacy. DynamIC Preprint 2018-3
Dongchen Li, Homoclinic Bifurcations that Give Rise to Heterodimensional Cycles near A Saddle-Focus Equilibrium. DynamIC Preprint 2016-3

2022

Serhiy Yanchuk, Matthias Wolfrum, Tiago Pereira, and Dmitry Turaev, Absolute stability and absolute hyperbolicity in systems with discrete time-delays, Journal of Differential Equations 318(2022), 323−343. Article MathSciNet

2021

Iacopo P. Longo, Carmen Núñez, Rafael Obaya, and Martin Rasmussen, Rate-induced tipping and saddle-node bifurcation for quadratic differential equations with nonautonomous asymptotic dynamics, SIAM Journal on Applied Dynamical Systems 20, 1 (2021), 500−540. Article MathSciNet Preprint
Moussa Ndour, Kathrin Padberg-Gehle, and Martin Rasmussen, Spectral early-warning signals for sudden changes in time-dependent flow patterns., Fluids 6(2021), 49. Article Preprint

2020

Jeroen S. W. Lamb, Mauricio F. S. Lima, Ricardo M. Martins, Marco Antonio Teixeira, and Jiazhong Yang, On the Hamiltonian structure of normal forms at elliptic equilibria of reversible vector fields in $\BbbR^4$, Journal of Differential Equations 269, 12 (2020), 11366−11395. Article MathSciNet Preprint

2019

Manuela A. D. Aguiar, Ana Dias, and Michael J. Field, Feedforward networks: adaptation, feedback, and synchrony, Journal of Nonlinear Science 29, 3 (2019), 1129−1164. Article MathSciNet Preprint
Pierre Berger and Dmitry Turaev, On Herman's positive entropy conjecture, Advances in Mathematics 349(2019), 1234−1288. Article MathSciNet
Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Bifurcation analysis of a stochastically driven limit cycle, Communications in Mathematical Physics 365, 3 (2019), 935−942. Article MathSciNet Preprint
Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Conditioned Lyapunov exponents for random dynamical systems, Transactions of the American Mathematical Society 372, 9 (2019), 6343−6370. Article MathSciNet Preprint

2018

Thai Son Doan, Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Hopf bifurcation with additive noise, Nonlinearity 31, 10 (2018), 4567−4601. Article MathSciNet Preprint
Jürgen Knobloch, Jeroen S. W. Lamb, and Kevin N. Webster, Shift dynamics near non-elementary T-points with real eigenvalues, Journal of Difference Equations and Applications 24, 4 (2018), 609−654. Article MathSciNet Preprint
Christian Kuehn, Giuseppe Malavolta, and Martin Rasmussen, Early-warning signals for bifurcations in random dynamical systems with bounded noise, Journal of Mathematical Analysis and Applications 464, 1 (2018), 58−77. Article MathSciNet Preprint

2017

Masayuki Asaoka, Katsutoshi Shinohara, and Dmitry Turaev, Degenerate behavior in non-hyperbolic semigroup actions on the interval: fast growth of periodic points and universal dynamics, Mathematische Annalen 368, 3−4 (2017), 1277−1309. Article MathSciNet
Mark Callaway, Thai Son Doan, Jeroen S. W. Lamb, and Martin Rasmussen, The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise, Annales de l'Institut Henri Poincaré Probabilités et Statistiques 53, 4 (2017), 1548−1574. Article MathSciNet Preprint
Deniz Eroglu, Jeroen S.W. Lamb, and Tiago Pereira, Synchronisation of chaos and its applications, Contemporary Physics 58, 3 (2017), 207−243. Article
Alexander S. Gonchenko, Sergey V. Gonchenko, Alexey O. Kazakov, and Dmitry Turaev, On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators, Physica D 350(2017), 45−57. Article MathSciNet
Dongchen Li and Dmitry Turaev, Existence of heterodimensional cycles near Shilnikov loops in systems with a $\BbbZ_2$ symmetry, Discrete and Continuous Dynamical Systems A 37, 8 (2017), 4399−4437. Article MathSciNet Preprint
Ivan I. Ovsyannikov and Dmitry Turaev, Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model, Nonlinearity 30, 1 (2017), 115−137. Article MathSciNet

2016

Fabio Bagarello, Anna Maria Cherubini, and Francesco Oliveri, An operatorial description of desertification, SIAM Journal on Applied Mathematics 76, 2 (2016), 479−499. Article MathSciNet Preprint
William Giles, Jeroen S.W. Lamb, and Dmitry Turaev, On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems, Nonlinearity 29, 10 (2016), 3148−3173. Article MathSciNet Preprint

2015

Vasso Anagnostopoulou, Tobias Jäger, and Gerhard Keller, A model for the nonautonomous Hopf bifurcation, Nonlinearity 28, 7 (2015), 2587−2616. MathSciNet Preprint
Henk Bruin and Sebastian van Strien, Monotonicity of entropy for real multimodal maps, Journal of the American Mathematical Society 28, 1 (2015), 1−61. Article MathSciNet
Thai Son Doan, Martin Rasmussen, and Peter E. Kloeden, The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor, Discrete and Continuous Dynamical Systems B 20, 3 (2015), 875−887. Article MathSciNet Preprint
Boumediene Hamzi, Jeroen S. W. Lamb, and Debra Lewis, A characterization of normal forms for control systems, Journal of Dynamical and Control Systems 21, 2 (2015), 273−284. Article MathSciNet
Jeroen S. W. Lamb, Martin Rasmussen, and Christian S. Rodrigues, Topological bifurcations of minimal invariant sets for set-valued dynamical systems, Proceedings of the American Mathematical Society 143, 9 (2015), 3927−3937. Article MathSciNet Preprint
Ivan I. Ovsyannikov, Dmitry Turaev, and Sergey Zelik, Bifurcation to chaos in the complex Ginzburg-Landau equation with large third-order dispersion, Modelirovanie i Analiz Informatsionnykh Sistem. Modeling and Analysis of Information Systems 22, 3 (2015), 327−336. Article MathSciNet Preprint
Jan Philipp Pade and Tiago Pereira, Improving network structure can lead to functional failures, Scientific Reports 5(2015), 9968. Article Preprint
Lasse Rempe-Gillen and Sebastian van Strien, Density of hyperbolicity for classes of real transcendental entire functions and circle maps, Duke Mathematical Journal 164, 6 (2015), 1079−1137. Article MathSciNet
Jake Stroud, Mauricio Barahona, and Tiago Pereira, Dynamics of cluster synchronisation in modular networks: implications for structural and functional networks, in: Applications of chaos and nonlinear dynamics in science and engineering, Understanding Complex Systems, 107−130, Springer, Cham, 2015. MathSciNet Preprint
Dmitry Turaev, Maps close to identity and universal maps in the Newhouse domain, Communications in Mathematical Physics 335, 3 (2015), 1235−1277. Article MathSciNet Preprint

2014

Valentin S. Afraimovich, Sergey V. Gonchenko, Lev M. Lerman, Andrey L. Shilnikov, and Dmitry Turaev, Scientific heritage of L. P. Shilnikov, Regular and Chaotic Dynamics 19, 4 (2014), 435−460. Article MathSciNet
Alexander Gonchenko, Sergey V. Gonchenko, Alexey Kazakov, and Dmitry Turaev, Simple scenarios of onset of chaos in three-dimensional maps, International Journal of Bifurcation and Chaos 24, 8 (2014), 1440005, 25. Article MathSciNet Preprint
Serey V. Gonchenko, Olga V. Gordeeva, Valery I. Lukyanov, and Ivan I. Ovsyannikov, On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node, Regular and Chaotic Dynamics 19, 4 (2014), 461−473. Article MathSciNet
Sergey V. Gonchenko, Jeroen S. W. Lamb, Isabel Rios, and Dmitry Turaev, Attractors and repellers in the neighborhood of elliptic points of reversible systems, Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 454, 4 (2014), 375−378. MathSciNet
Sergey V. Gonchenko, Ivan I. Ovsyannikov, and Joan C. Tatjer, Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points, Regular and Chaotic Dynamics 19, 4 (2014), 495−505. Article MathSciNet
Leonid Pavlovich Shilnikov, Andrey L. Shilnikov, and Dmitry V. Turaev, Showcase of blue sky catastrophes, International Journal of Bifurcation and Chaos 24, 8 (2014), 1440003, 10. Article MathSciNet Preprint
Dmitry Turaev, Hyperbolic sets near homoclinic loops to a saddle for systems with a first integral, Regular and Chaotic Dynamics 19, 6 (2014), 681−693. Article MathSciNet Preprint
Yong Zou, Tiago Pereira, Michael Small, Zonghua Liu, and Jürgen Kurths, Basin of attraction determines hysteresis in explosive synchronization, Physical Review Letters 112(2014), 114102. Article

2013

Henk Bruin and Sebastian van Strien, On the structure of isentropes of polynomial maps, Dynamical Systems 28, 3 (2013), 381−392. Article MathSciNet
Sergey V. Gonchenko, Alexander S. Gonchenko, Ivan I. Ovsyannikov, and Dmitry Turaev, Examples of Lorenz-like attractors in Hénon-like maps, Mathematical Modelling of Natural Phenomena 8, 5 (2013), 48−70. Article MathSciNet
Sergey V. Gonchenko and Ivan I. Ovsyannikov, On global bifurcations of three-dimensional diffeomorphisms leading to Lorenz-like attractors, Mathematical Modelling of Natural Phenomena 8, 5 (2013), 71−83. Article MathSciNet
Peter E. Kloeden, Christian Pötzsche, and Martin Rasmussen, Discrete-time nonautonomous dynamical systems, in: Stability and bifurcation theory for non-autonomous differential equations, Lecture Notes in Mathematics, 35−102, Springer, Heidelberg, 2013. Article MathSciNet

2012

Vasso Anagnostopoulou and Tobias Jäger, Nonautonomous saddle-node bifurcations: random and deterministic forcing, Journal of Differential Equations 253, 2 (2012), 379−399. Article MathSciNet
Adriana Buică, Jaume Llibre, and Oleg Makarenkov, Bifurcations from nondegenerate families of periodic solutions in Lipschitz systems, Journal of Differential Equations 252, 6 (2012), 3899−3919. Article MathSciNet
Sergey V. Gonchenko, Ivan I. Ovsyannikov, and Dmitry Turaev, On the effect of invisibility of stable periodic orbits at homoclinic bifurcations, Physica D 241, 13 (2012), 1115−1122. Article MathSciNet
Lev M. Lerman and Dmitry Turaev, Breakdown of symmetry in reversible systems, Regular and Chaotic Dynamics 17, 3−4 (2012), 318−336. Article MathSciNet
Oleg Makarenkov and Jeroen S. W. Lamb, Dynamics and bifurcations of nonsmooth systems: a survey, Physica D 241, 22 (2012), 1826−1844. Article MathSciNet

2011

Ale Jan Homburg, Alice C. Jukes, Jürgen Knobloch, and Jeroen S. W. Lamb, Bifurcation from codimension one relative homoclinic cycles, Transactions of the American Mathematical Society 363, 11 (2011), 5663−5701. Article MathSciNet
Mikhail Kamenskii, Oleg Makarenkov, and Paolo Nistri, An alternative approach to study bifurcation from a limit cycle in periodically perturbed autonomous systems, Journal of Dynamics and Differential Equations 23, 3 (2011), 425−435. Article MathSciNet
Oleg Makarenkov, Luisa Malaguti, and Paolo Nistri, On the behavior of periodic solutions of planar autonomous Hamiltonian systems with multivalued periodic perturbations, Zeitschrift für Analysis und ihre Anwendungen 30, 2 (2011), 129−144. Article MathSciNet
Gheorghe Tigan and Dmitry Turaev, Analytical search for homoclinic bifurcations in the Shimizu-Morioka model, Physica D 240, 12 (2011), 985−989. Article MathSciNet
Dmitry Turaev, Diffeomorphisms which cannot be topologically conjugate to diffeomorphisms of a higher smoothness, Ergodic Theory and Dynamical Systems 31, 2 (2011), 563−569. Article MathSciNet

2010

Martin Rasmussen, Finite-time attractivity and bifurcation for nonautonomous differential equations, Differential Equations and Dynamical Systems 18, 1−2 (2010), 57−78. Article MathSciNet
Dmitry Turaev, Richness of chaos in the absolute Newhouse domain, in: Proceedings of the International Congress of Mathematicians. Volume III, 1804−1815, Hindustan Book Agency, New Delhi, 2010. MathSciNet

2009

Pietro-Luciano Buono, Martin Helmer, and Jeroen S. W. Lamb, On the zero set of G-equivariant maps, Mathematical Proceedings of the Cambridge Philosophical Society 147, 3 (2009), 735−755. Article MathSciNet
Shangjiang Guo, Jeroen S. W. Lamb, and Bob W. Rink, Branching patterns of wave trains in the FPU lattice, Nonlinearity 22, 2 (2009), 283−299. Article MathSciNet

2008

Robert E. Beardmore and Kevin N. Webster, Normal forms, quasi-invariant manifolds, and bifurcations of nonlinear difference-algebraic equations, SIAM Journal on Mathematical Analysis 40, 1 (2008), 413−441. Article MathSciNet
Robert E. Beardmore and Kevin N. Webster, A Hopf bifurcation theorem for singular differential-algebraic equations, Mathematics and Computers in Simulation 79, 4 (2008), 1383−1395. Article MathSciNet
Pietro-Luciano Buono, Jeroen S. W. Lamb, and R. Mark Roberts, Bifurcation and branching of equilibria in reversible-equivariant vector fields, Nonlinearity 21, 4 (2008), 625−660. Article MathSciNet
Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, On dynamical properties of multidimensional diffeomorphisms from Newhouse regions. I, Nonlinearity 21, 5 (2008), 923−972. Article MathSciNet
Shangjiang Guo and Jeroen S. W. Lamb, Equivariant Hopf bifurcation for neutral functional differential equations, Proceedings of the American Mathematical Society 136, 6 (2008), 2031−2041. Article MathSciNet
Ale Jan Homburg, Alice C. Jukes, Jürgen Knobloch, and Jeroen S. W. Lamb, Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows, Bulletin of the Belgian Mathematical Society. Simon Stevin 15, 5 (2008), 833−850. Article MathSciNet
Dmitry Turaev and Leonid P. Shilnikov, Pseudohyperbolicity and the problem of the periodic perturbation of Lorenz-type attractors, Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 418, 1 (2008), 23−27. Article MathSciNet

2007

Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps, Nonlinearity 20, 2 (2007), 241−275. Article MathSciNet
Jeroen S. W. Lamb and Ian Melbourne, Normal form theory for relative equilibria and relative periodic solutions, Transactions of the American Mathematical Society 359, 9 (2007), 4537−4556. Article MathSciNet
Martin Rasmussen, Nonautonomous bifurcation patterns for one-dimensional differential equations, Journal of Differential Equations 234, 1 (2007), 267−288. Article MathSciNet
Martin Rasmussen, Attractivity and bifurcation for nonautonomous dynamical systems, Lecture Notes in Mathematics 1907, Springer, Berlin, 2007. MathSciNet

2006

Ana Paula S. Dias and Jeroen S. W. Lamb, Local bifurcation in symmetric coupled cell networks: linear theory, Physica D 223, 1 (2006), 93−108. Article MathSciNet
Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, Homoclinic tangencies of arbitrary order in conservative two-dimensional mappings, Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 407, 3 (2006), 299−303. MathSciNet
Ale Jan Homburg and Jeroen S. W. Lamb, Symmetric homoclinic tangles in reversible systems, Ergodic Theory and Dynamical Systems 26, 6 (2006), 1769−1789. Article MathSciNet
Martin Rasmussen, Towards a bifurcation theory for nonautonomous difference equations, Journal of Difference Equations and Applications 12, 3−4 (2006), 297−312. Article MathSciNet

2005

Claudio A. Buzzi and Jeroen S. W. Lamb, Reversible Hamiltonian Liapunov center theorem, Discrete and Continuous Dynamical Systems B 5, 1 (2005), 51−66. MathSciNet
Claudio A. Buzzi and Jeroen S. W. Lamb, Reversible equivariant Hopf bifurcation, Archive for Rational Mechanics and Analysis 175, 1 (2005), 39−84. Article MathSciNet
Sergey V. Gonchenko, Ivan I. Ovsyannikov, Carles Simó, and Dmitry Turaev, Three-dimensional Hénon-like maps and wild Lorenz-like attractors, International Journal of Bifurcation and Chaos 15, 11 (2005), 3493−3508. Article MathSciNet
Jeroen S. W. Lamb, Marco-Antonio Teixeira, and Kevin N. Webster, Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in R^3, Journal of Differential Equations 219, 1 (2005), 78−115. Article MathSciNet
Andrey Shilnikov, Leonid P. Shilnikov, and Dmitry Turaev, Blue-sky catastrophe in singularly perturbed systems, Moscow Mathematical Journal 5, 1 (2005), 269−282. MathSciNet
Dmitry Turaev, An example of a resonant homoclinic loop of infinite cyclicity, Moscow Mathematical Journal 5, 1 (2005), 283−293. MathSciNet

2004

Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, The existence of a countable set of elliptic periodic trajectories in four-dimensional symplectic mappings with a homoclinic tangency, Trudy Matematicheskogo Instituta Imeni V. A. Steklova. Rossiĭskaya Akademiya Nauk 244, Din. Sist. i Smezhnye Vopr. Geom. (2004), 115−142. MathSciNet
Jeroen S. W. Lamb and Oleg V. Stenkin, Newhouse regions for reversible systems with infinitely many stable, unstable and elliptic periodic orbits, Nonlinearity 17, 4 (2004), 1217−1244. Article MathSciNet
Andrey Shilnikov, Leonid P. Shilnikov, and Dmitry Turaev, On some mathematical topics in classical synchronization. A tutorial, International Journal of Bifurcation and Chaos 14, 7 (2004), 2143−2160. Article MathSciNet

2003

Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, On the dynamic properties of diffeomorphisms with homoclinic tangencies, Sovremennaya Matematika i ee Prilozheniya , 7 (2003), 91−117. MathSciNet
Igor Hoveijn, Jeroen S. W. Lamb, and R. Mark Roberts, Normal forms and unfoldings of linear systems in eigenspaces of (anti)-automorphisms of order two, Journal of Differential Equations 190, 1 (2003), 182−213. Article MathSciNet
Jeroen S. W. Lamb, Ian Melbourne, and Claudia Wulff, Bifurcation from periodic solutions with spatiotemporal symmetry, including resonances and mode interactions, Journal of Differential Equations 191, 2 (2003), 377−407. Article MathSciNet
Dmitry Turaev, Polynomial approximations of symplectic dynamics and richness of chaos in non-hyperbolic area-preserving maps, Nonlinearity 16, 1 (2003), 123−135. Article MathSciNet
Dmitry Turaev and Sergey Zelik, Homoclinic bifurcations and dimension of attractors for damped nonlinear hyperbolic equations, Nonlinearity 16, 6 (2003), 2163−2198. Article MathSciNet
Kevin N. Webster and John N. Elgin, Asymptotic analysis of the Michelson system, Nonlinearity 16, 6 (2003), 2149−2162. Article MathSciNet

2001

Leonid P. Shilnikov, Andrey L. Shilnikov, Dmitry Turaev, and Leon O. Chua, Methods of qualitative theory in nonlinear dynamics. Part II, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises 5, World Scientific, River Edge, New Jersey, 2001. Article MathSciNet
Dmitry Turaev, Multi-pulse homoclinic loops in systems with a smooth first integral, in: Ergodic theory, analysis, and efficient simulation of dynamical systems, 691−716, Springer, Berlin, 2001. MathSciNet
Claudia Wulff, Jeroen S. W. Lamb, and Ian Melbourne, Bifurcation from relative periodic solutions, Ergodic Theory and Dynamical Systems 21, 2 (2001), 605−635. Article MathSciNet

2000

Jeroen S. W. Lamb, Ian Melbourne, and Claudia Wulff, Bifurcation from periodic and relative periodic solutions in equivariant dynamical systems, in: International Conference on Differential Equations, Vol. 1, 2 (Berlin, 1999), 175−185, World Scientific, River Edge, New Jersey, 2000. MathSciNet
Jeroen S. W. Lamb and Claudia Wulff, Pinning and locking of discrete waves, Physics Letters A 267, 2−3 (2000), 167−173. Article MathSciNet
Mikhail V. Shashkov and Dmitry Turaev, A proof of Shilnikov's theorem for C^1-smooth dynamical systems, in: Methods of qualitative theory of differential equations and related topics, American Mathematical Society Translations, Series 2, 149−163, American Mathematical Society, Providence, 2000. MathSciNet
Leonid P. Shilnikov and Dmitry V. Turaev, A new simple bifurcation of a periodic orbit of blue sky catastrophe type, in: Methods of qualitative theory of differential equations and related topics, American Mathematical Society Translations, Series 2, 165−188, American Mathematical Society, Providence, 2000. MathSciNet

1999

Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, Homoclinic tangencies of arbitrary order in Newhouse domains, in: Dynamical systems (Russian) (Moscow, 1998), Itogi Nauki Tekh. Ser. Sovrem. Mat. Prilozh. Temat. Obz., 69−128, Vseross. Inst. Nauchn. i Tekhn. Inform. (VINITI), Moscow, 1999. MathSciNet
Jeroen S. W. Lamb and Ian Melbourne, Bifurcation from discrete rotating waves, Archive for Rational Mechanics and Analysis 149, 3 (1999), 229−270. Article MathSciNet
Jeroen S. W. Lamb and Ian Melbourne, Bifurcation from periodic solutions with spatiotemporal symmetry, in: Pattern formation in continuous and coupled systems (Minneapolis, MN, IMA Vol. Math. Appl., 175−191, Springer, New York, 1999. Article MathSciNet
V. Pisarevskii, Andrey Shilnikov, and Dmitry Turaev, Asymptotic normal forms for equilibria with a triplet of zero characteristic exponents in systems with symmetry, in: Iteration theory (ECIT 96) (Urbino), Grazer Mathematische Berichte, 291−300, Karl-Franzens-Universität Graz, Graz, 1999. MathSciNet
Mikhail V. Shashkov and Dmitry Turaev, An existence theorem of smooth nonlocal center manifolds for systems close to a system with a homoclinic loop, Journal of Nonlinear Science 9, 5 (1999), 525−573. Article MathSciNet

1998

Leonid A. Bunimovich and Dmitry Turaev, Localized solutions in lattice systems and their bifurcations caused by spatial interactions, Nonlinearity 11, 6 (1998), 1539−1545. Article MathSciNet
Bernold Fiedler and Dmitry Turaev, Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions, Archive for Rational Mechanics and Analysis 145, 2 (1998), 129−159. Article MathSciNet
Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, Elliptic periodic orbits near a homoclinic tangency in four-dimensional symplectic maps and Hamiltonian systems with three degrees of freedom, Regular and Chaotic Dynamics 3, 4 (1998), 3−26. Article MathSciNet
Jeroen S. W. Lamb, k-symmetry and return maps of spacetime symmetric flows, Nonlinearity 11, 3 (1998), 601−629. Article MathSciNet
Jeroen S. W. Lamb and John A. G. Roberts, Time-reversal symmetry in dynamical systems: a survey, Physica D 112, 1−2 (1998), 1−39. Article MathSciNet
V. Pisarevskii, Andrey Shilnikov, and Dmitry Turaev, Asymptotic normal forms for equilibria with a triplet of zero characteristic exponents in systems with symmetry, Regulyarnaya & Khaoticheskaya Dinamika. Regular & Chaotic Dynamics 3, 1 (1998), 19−27. MathSciNet
Leonid P. Shilnikov, Andrey L. Shilnikov, Dmitry V. Turaev, and Leon O. Chua, Methods of qualitative theory in nonlinear dynamics. Part I, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises 4, World Scientific, River Edge, New Jersey, 1998. Article MathSciNet
Dmitry Turaev and Leonid P. Shilnikov, An example of a wild strange attractor, Rossiĭskaya Akademiya Nauk. Matematicheskiĭ Sbornik 189, 2 (1998), 137−160. Article MathSciNet

1997

Sergey V. Gonchenko, Leonid P. Shilnikov, Oleg V. Stenkin, and Dmitry Turaev, Bifurcations of systems with structurally unstable homoclinic orbits and moduli of omega-equivalence, Computers & Mathematics with Applications 34, 2−4 (1997), 111−142. Article MathSciNet
Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, Quasiattractors and homoclinic tangencies, Computers & Mathematics with Applications 34, 2−4 (1997), 195−227. Article MathSciNet
Sergey V. Gonchenko, Dmitry Turaev, Pierre Gaspard, and Gregoire Nicolis, Complexity in the bifurcation structure of homoclinic loops to a saddle-focus, Nonlinearity 10, 2 (1997), 409−423. Article MathSciNet
Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, On Newhouse domains of two-dimensional diffeomorphisms that are close to a diffeomorphism with a structurally unstable heteroclinic contour, Trudy Matematicheskogo Instituta Imeni V. A. Steklova. Rossiĭskaya Akademiya Nauk 216, Din. Sist. i Smezhnye Vopr. (1997), 76−125. MathSciNet
Leonid P. Shilnikov and Dmitry Turaev, Super-homoclinic orbits and multi-pulse homoclinic loops in Hamiltonian systems with discrete symmetries, Regulyarnaya & Khaoticheskaya Dinamika. Regular & Chaotic Dynamics 2, 3−4 (1997), 126−138. MathSciNet
Leonid P. Shilnikov and Dmitry Turaev, Simple bifurcations leading to hyperbolic attractors, Computers & Mathematics with Applications 34, 2−4 (1997), 173−193. Article MathSciNet

1996

Bernold Fiedler and Dmitry Turaev, Coalescence of reversible homoclinic orbits causes elliptic resonance, International Journal of Bifurcation and Chaos 6, 6 (1996), 1007−1027. Article MathSciNet
Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, Bifurcations of two-dimensional diffeomorphisms with non-rough homoclinic contours, Journal of Technical Physics 37, 3−4 (1996), 349−352. MathSciNet
Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits, Chaos 6, 1 (1996), 15−31. Article MathSciNet
Sergey V. Gonchenko, Oleg V. Stenkin, and Dmitry Turaev, Complexity of homoclinic bifurcations and $\Omega$-moduli, International Journal of Bifurcation and Chaos 6, 6 (1996), 969−989. Article MathSciNet
Jeroen S. W. Lamb, Local bifurcations in k-symmetric dynamical systems, Nonlinearity 9, 2 (1996), 537−557. Article MathSciNet
Mikhail V. Shashkov and Dmitry V. Turaev, On the complex bifurcation set for a system with simple dynamics, International Journal of Bifurcation and Chaos 6, 5 (1996), 949−968. Article MathSciNet
Dmitry Turaev, On dimension reduction near homoclinic and heteroclinic cycles, Journal of Technical Physics 37, 3−4 (1996), 437−440. MathSciNet
Dmitry Turaev, On dimension of non-local bifurcational problems, International Journal of Bifurcation and Chaos 6, 5 (1996), 919−948. Article MathSciNet

1995

Jeroen S. W. Lamb and Hans W. Capel, Local bifurcations on the plane with reversing point group symmetry, Chaos, Solitons and Fractals 5, 2 (1995), 271−293. Article MathSciNet
John A. G. Roberts and Jeroen S. W. Lamb, Self-similarity of period-doubling branching in 3-D reversible mappings, Physica D 82, 4 (1995), 317−332. Article MathSciNet
Dmitry Turaev and Leonid P. Shilnikov, Blue sky catastrophes, Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 342, 5 (1995), 596−599. MathSciNet

1993

Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, On models with nonrough Poincaré homoclinic curves, Physica D 62, 1−4 (1993), 1−14. Article MathSciNet
Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, Dynamical phenomena in multidimensional systems with a structurally unstable homoclinic Poincaré curve, Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 330, 2 (1993), 144−147. MathSciNet
Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, On the existence of Newhouse regions in a neighborhood of systems with a structurally unstable homoclinic Poincaré curve (the multidimensional case), Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 329, 4 (1993), 404−407. MathSciNet
Andrey L. Shilnikov, Leonid P. Shilnikov, and Dmitry Turaev, Normal forms and Lorenz attractors, International Journal of Bifurcation and Chaos 3, 5 (1993), 1123−1139. Article MathSciNet

1992

Alexander S. Dmitriev, Yuri A. Komlev, and Dmitry Turaev, Bifurcation phenomena in the 1:1 resonant horn for the forced van der Pol-Duffing equation, International Journal of Bifurcation and Chaos 2, 1 (1992), 93−100. Article MathSciNet
Jeroen S. W. Lamb, The ferro-antiferro bifurcation transition in a microscopic model with incommensurate phases, Journal of Physics A 25(1992), 355−365.

1991

Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, On models with a structurally unstable homoclinic Poincaré curve, in: Methods in qualitative theory and bifurcation theory (Russian), 36−61, Nizhegorod. Gos. Univ., Nizhniy Novgorod, 1991. MathSciNet
Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, Models with a structurally unstable homoclinic Poincaré curve, Doklady Akademii Nauk SSSR 320, 2 (1991), 269−272. MathSciNet

1989

Patrick Bonckaert, Freddy Dumortier, and Sebastian van Strien, Singularities of vector fields on R^3 determined by their first nonvanishing jet, Ergodic Theory and Dynamical Systems 9, 2 (1989), 281−308. Article MathSciNet

1988

Dmitry Turaev, Bifurcations of a homoclinic figure eight of a multidimensional saddle, Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk 43, 5(263) (1988), 223−224. Article MathSciNet

1987

Welington de Melo and Sebastian van Strien, Diffeomorphisms on surfaces with a finite number of moduli, Ergodic Theory and Dynamical Systems 7, 3 (1987), 415−462. Article MathSciNet
Sebastian van Strien, Normal hyperbolicity and linearisability, Inventiones Mathematicae 87, 2 (1987), 377−384. Article MathSciNet
Sebastian van Strien and Geovan Tavares dos Santos, Moduli of stability for germs of homogeneous vectorfields on R^3, Journal of Differential Equations 69, 1 (1987), 63−84. Article MathSciNet

1986

Dmitry Turaev and Leonid P. Shilnikov, Bifurcations of quasi-attractors of torus-chaos, in: Mathematical mechanisms of turbulence (Russian), 113−121, iii, Akad. Nauk Ukrain. SSR Inst. Mat., Kiev, 1986. MathSciNet
Dmitry Turaev and Leonid P. Shilnikov, Bifurcation of a homoclinic figure eight saddle with a negative saddle value, Doklady Akademii Nauk SSSR 290, 6 (1986), 1301−1304. MathSciNet

1985

Dmitry Turaev, Bifurcations of two-dimensional dynamical systems that are close to a system with two separatrix loops, Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk 40, 2(242) (1985), 203−204. MathSciNet

1984

Dmitry Turaev, A case of bifurcation from a contour formed by homoclinic curves emerging from a saddle, in: Methods of the qualitative theory of differential equations (Russian), 162−175, 203, Gorkov. Gos. Univ., Gorki, 1984. MathSciNet

1983

Henk Broer and Sebastian van Strien, Infinitely many moduli of strong stability in divergence free unfoldings of singularities of vector fields, in: Geometric dynamics, Lecture Notes in Mathematics, 39−59, Springer, Berlin, 1983. Article MathSciNet

1981

Welington de Melo, Jacob Palis, and Sebastian van Strien, Characterising diffeomorphisms with modulus of stability one, in: Dynamical systems and turbulence, Lecture Notes in Mathematics, 266−285, Springer, Berlin, 1981. MathSciNet
Sebastian van Strien, Saddle connections of arcs of diffeomorphisms: moduli of stability, in: Dynamical systems and turbulence, Lecture Notes in Mathematics, 352−365, Springer, Berlin, 1981. MathSciNet
Sebastian van Strien, On the bifurcations creating horseshoes, in: Dynamical systems and turbulence, Lecture Notes in Mathematics, 316−351, Springer, Berlin, 1981. MathSciNet