Publications – Dynamical Systems at Imperial College London (DynamIC)

Sergey V. Gonchenko, Alexey Kazakov, Dmitry Turaev, and Andrey L. Shilnikov, Leonid Shilnikov and mathematical theory of dynamical chaos, Chaos 32, 1 (2022), Paper No. 010402, 15. Article MathSciNet

2021

A. S. Gonchenko, Sergey V. Gonchenko, and Dmitry Turaev, Doubling of invariant curves and chaos in three-dimensional diffeomorphisms, Chaos 31, 11 (2021), Paper No. 113130, 17. Article MathSciNet
Sergey V. Gonchenko, Alexey Kazakov, and Dmitry Turaev, Wild pseudohyperbolic attractor in a four-dimensional Lorenz system, Nonlinearity 34, 4 (2021), 2018−2047. Article MathSciNet

2020

Dongchen Li and Dmitry Turaev, Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors, Nonlinearity 33, 3 (2020), 971−1015. Article MathSciNet

2019

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

2018

Maciej J. Capiński, Dmitry Turaev, and Piotr Zgliczyński, Computer assisted proof of the existence of the Lorenz attractor in the Shimizu-Morioka system, Nonlinearity 31, 12 (2018), 5410−5440. Article MathSciNet
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

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
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
Sergey V. Gonchenko and Dmitry Turaev, On three types of dynamics and the notion of attractor, Trudy Matematicheskogo Instituta Imeni V. A. Steklova. Rossiuiskaya Akademiya Nauk 297, Poryadok i Khaos v Dinamicheskikh Sistemakh (2017), 133−157. Article MathSciNet
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

2015

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
Tiago Pereira and Dmitry Turaev, Fast Fermi acceleration and entropy growth, Mathematical Modelling of Natural Phenomena 10, 3 (2015), 31−47. Article MathSciNet Preprint
Tiago Pereira and Dmitry Turaev, Exponential energy growth in adiabatically changing Hamiltonian systems, Physical Review E 91, 1 (2015), 010910(R), 4. Article MathSciNet Preprint
Kushal Shah, Vassili Gelfreich, Vered Rom-Kedar, and Dmitry Turaev, Leaky Fermi accelerators, Physical Review E 91, 6 (2015), 062920, 7. Article 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
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
Dmitry Turaev, Christopher Warner, and Sergey Zelik, Energy growth for a nonlinear oscillator coupled to a monochromatic wave, Regular and Chaotic Dynamics 19, 4 (2014), 513−522. Article MathSciNet

2013

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

2012

Vassili Gelfreich, Vered Rom-Kedar, and Dmitry Turaev, Fermi acceleration and adiabatic invariants for non-autonomous billiards, Chaos. An Interdisciplinary Journal of Nonlinear Science 22, 3 (2012), 033116, 21. Article MathSciNet Preprint
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
Vered Rom-Kedar and Dmitry Turaev, Billiards: a singular perturbation limit of smooth Hamiltonian flows, Chaos. An Interdisciplinary Journal of Nonlinear Science 22, 2 (2012), 026102, 21. Article MathSciNet Preprint

2011

Gheorghe Tigan and Dmitry Turaev, Analytical search for homoclinic bifurcations in the Shimizu-Morioka model, Physica D 240, 12 (2011), 985−989. Article MathSciNet

2010

Vassili Gelfreich and Dmitry Turaev, Universal dynamics in a neighborhood of a generic elliptic periodic point, Regular and Chaotic Dynamics 15, 2−3 (2010), 159−164. Article MathSciNet
Vered Rom-Kedar and Dmitry Turaev, The symmetric parabolic resonance, Nonlinearity 23, 6 (2010), 1325−1351. Article MathSciNet
Kushal Shah, Dmitry Turaev, and Vered Rom-Kedar, Exponential energy growth in a Fermi accelerator, Physical Review E 81, 5 (2010), 056205, 6. 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
Dmitry Turaev and Sergey Zelik, Analytical proof of space-time chaos in Ginzburg-Landau equations, Discrete and Continuous Dynamical Systems A 28, 4 (2010), 1713−1751. Article MathSciNet

2009

Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors, Regular and Chaotic Dynamics 14, 1 (2009), 137−147. Article MathSciNet

2008

Vassili Gelfreich and Dmitry Turaev, Unbounded energy growth in Hamiltonian systems with a slowly varying parameter, Communications in Mathematical Physics 283, 3 (2008), 769−794. Article MathSciNet
Vassili Gelfreich and Dmitry Turaev, Fermi acceleration in non-autonomous billiards, Journal of Physics A 41, 21 (2008), 212003, 6. 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
Anna Rapoport, Vered Rom-Kedar, and Dmitry Turaev, Stability in high dimensional steep repelling potentials, Communications in Mathematical Physics 279, 2 (2008), 497−534. 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
Anna Rapoport, Vered Rom-Kedar, and Dmitry Turaev, Approximating multi-dimensional Hamiltonian flows by billiards, Communications in Mathematical Physics 272, 3 (2007), 567−600. Article MathSciNet

2006

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

2005

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

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
Sam Gratrix and John N. Elgin, Pointwise dimensions of the Lorenz attractor, Physical Review Letters 92, 1 (2004), 014101, 4. Article 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
Stefano Luzzatto and Marcelo Viana, Exclusions of parameter values in Hénon-type systems, Rossiĭskaya Akademiya Nauk. Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk 58, 6(354) (2003), 3−44. Article MathSciNet
Jaroslav Stark and Kate Hardy, Chaos: Useful at Last, Science 301(2003), 1192−1193.
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 Vered Rom-Kedar, Soft billiards with corners, Journal of Statistical Physics 112, 3−4 (2003), 765−813. 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

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
Vered Rom-Kedar and Dmitry Turaev, Big islands in dispersing billiard-like potentials, Physica D 130, 3−4 (1999), 187−210. Article MathSciNet

1998

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
Dmitry Turaev and Vered Rom-Kedar, On smooth Hamiltonian flows limited to ergodic billiards, in: Chaos, kinetics and nonlinear dynamics in fluids and plasmas (Carry-Le Rouet, 1997), Lecture Notes in Phyics, 17−50, Springer, Berlin, 1998. Article MathSciNet
Dmitry Turaev and Vered Rom-Kedar, Elliptic islands appearing in near-ergodic flows, Nonlinearity 11, 3 (1998), 575−600. 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
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

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

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

Vladimir M. Eleonskiĭ, Nikolai E. Kulagin, Dmitry Turaev, and Leonid P. Shilnikov, Classification of self-localized states of an electromagnetic field in a nonlinear medium, Doklady Akademii Nauk SSSR 309, 4 (1989), 848−852. MathSciNet
Dmitry Turaev and Leonid P. Shilnikov, Hamiltonian systems with homoclinic saddle curves, Doklady Akademii Nauk SSSR 304, 4 (1989), 811−814. 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

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