Publications – Dynamical Systems at Imperial College London (DynamIC)

Jeroen S. W. Lamb, Martin Rasmussen, and Wei Hao Tey, Attractors of Linear Maps with Bounded Noise. DynamIC Preprint 2023-2
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
Lea Oljaca, Peter Ashwin, and Martin Rasmussen, Measure and statistical attractors for nonautonomous dynamical systems. DynamIC Preprint 2022-3
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
Gabriel Fuhrmann and Maik Gröger, Constant length substitutions, iterated function systems and amorphic complexity. DynamIC Preprint 2019-3
Nikolaos Karaliolios, Invariant Distributions and local theory of quasiperiodic cocycles in T^d x SU(2). DynamIC Preprint 2016-10
Nikolaos Karaliolios, Differentiable Rigidity for quasiperiodic cocycles in compact Lie groups. DynamIC Preprint 2016-9
Alexander M. Henderson, Eric J. Olson, James C. Robinson, and Nicholas Sharples, Equi-homogeneity, Assouad dimension and non-autonomous dynamics. DynamIC Preprint 2014-7

2021

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
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

2020

Peter Giesl, Boumediene Hamzi, Martin Rasmussen, and Kevin Webster, Approximation of Lyapunov functions from noisy data, Journal of Computational Dynamics 7, 1 (2020), 57−81. Article MathSciNet Preprint

2019

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

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

2017

Anna Maria Cherubini, Jeroen S. W. Lamb, Martin Rasmussen, and Yuzuru Sato, A random dynamical systems perspective on stochastic resonance, Nonlinearity 30, 7 (2017), 2835−2853. Article MathSciNet Preprint
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
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

2016

Martin Rasmussen, Alan Hastings, Matthew J. Smith, Folashade B. Agusto, Benito M. Chen-Charpentier, Forrest M. Hoffman, Jiang Jiang, Katherine E. O. Todd-Brown, Ying Wang, Ying-Ping Wang, and Yiqi Luo, Transit times and mean ages for nonautonomous and autonomous compartmental systems, Journal of Mathematical Biology 73, 6−7 (2016), 1379−1398. 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
Thai Son Doan, Anke Kalauch, Markus Klose, and Stefan Siegmund, Stability of positive linear switched systems on ordered Banach spaces, Systems & Control Letters 75(2015), 14−19. 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

2014

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

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
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
Weixiao Shen and Sebastian van Strien, On stochastic stability of expanding circle maps with neutral fixed points, Dynamical Systems 28, 3 (2013), 423−452. 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
Peter Giesl and Martin Rasmussen, Areas of attraction for nonautonomous differential equations on finite time intervals, Journal of Mathematical Analysis and Applications 390, 1 (2012), 27−46. Article MathSciNet

2011

Stefan Liebscher, Jörg Härterich, Kevin N. Webster, and Marc Georgi, Ancient dynamics in Bianchi models: approach to periodic cycles, Communications in Mathematical Physics 305, 1 (2011), 59−83. Article MathSciNet
Oleg Makarenkov and Rafael Ortega, Asymptotic stability of forced oscillations emanating from a limit cycle, Journal of Differential Equations 250, 1 (2011), 39−52. Article MathSciNet

2010

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

Adriana Buică, Jaume Llibre, and Oleg Makarenkov, Asymptotic stability of periodic solutions for nonsmooth differential equations with application to the nonsmooth van der Pol oscillator, SIAM Journal on Mathematical Analysis 40, 6 (2009), 2478−2495. Article MathSciNet

2008

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
Martin Rasmussen, All-time Morse decompositions of linear nonautonomous dynamical systems, Proceedings of the American Mathematical Society 136, 3 (2008), 1045−1055. 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

Oleg Kozlovski, Weixiao Shen, and Sebastian van Strien, Density of hyperbolicity in dimension one, Annals of Mathematics 166, 1 (2007), 145−182. Article MathSciNet
Martin Rasmussen, Attractivity and bifurcation for nonautonomous dynamical systems, Lecture Notes in Mathematics 1907, Springer, Berlin, 2007. MathSciNet
Martin Rasmussen, Morse decompositions of nonautonomous dynamical systems, Transactions of the American Mathematical Society 359, 10 (2007), 5091−5115. Article MathSciNet

2006

Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Invariant manifolds as pullback attractors of nonautonomous differential equations, Discrete and Continuous Dynamical Systems A 15, 2 (2006), 579−596. Article MathSciNet

2005

Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Approximation of attractors of nonautonomous dynamical systems, Discrete and Continuous Dynamical Systems B 5, 2 (2005), 215−238. Article MathSciNet
Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Invariant manifolds as pullback attractors of nonautonomous difference equations, in: Proceedings of the Eighth International Conference on Difference Equations and Applications (S. Elaydi, G. Ladas, B. Aulbach, O. Dosly), 23−37, CRC, Boca Raton, 2005. 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
Stefano Luzzatto, Ian Melbourne, and Frederic Paccaut, The Lorenz attractor is mixing, Communications in Mathematical Physics 260, 2 (2005), 393−401. Article MathSciNet

2004

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

2001

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

1999

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

1998

Jeroen S. W. Lamb and Matthew Nicol, On symmetric attractors in reversible dynamical systems, Physica D 112, 1−2 (1998), 281−297. 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
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, and Dmitry Turaev, Quasiattractors and homoclinic tangencies, Computers & Mathematics with Applications 34, 2−4 (1997), 195−227. Article 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

Jeroen S. W. Lamb and Matthew Nicol, On symmetric omega-limit sets in reversible flows, in: Nonlinear Dynamical Systems and Chaos, Progress in Nonlinear Differential Equations and Their Applications, 103−120, Birkhäuser, Basel, 1996. MathSciNet

1993

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

1989

Jean-Marc Gambaudo, Sebastian van Strien, and Charles Tresser, Hénon-like maps with strange attractors: there exist C^\infty Kupka-Smale diffeomorphisms on S^2 with neither sinks nor sources, Nonlinearity 2, 2 (1989), 287−304. 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