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
Matheus M. Castro, Vincent P. H. Goverse, Jeroen S. W. Lamb, and Martin Rasmussen, On the quasi-ergodicity of absorbing Markov chains with unbounded transition densities, including random logistic maps with escape. DynamIC Preprint 2022-2
Gabriel Fuhrmann, Maik Gröger, and Alejandro Passeggi, The bifurcation set as a topological invariant for one-dimensional dynamics. DynamIC Preprint 2019-2
Trevor Clark and Sebastian van Strien, Quasisymmetric rigidity in one-dimensional dynamics. DynamIC Preprint 2018-10
Trevor Clark, Edson de Faria, and Sebastian van Strien, Dynamics of asymptotically holomorphic polynomial-like maps. DynamIC Preprint 2018-9
Björn Winckler, The Lorenz Renormalization Conjecture. DynamIC Preprint 2018-8
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
Davoud Cheraghi and Mitsuhiro Shishikura, Satellite renormalization of quadratic polynomials. DynamIC Preprint 2015-5

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

2020

Oleg Kozlovski and Sebastian van Strien, Asymmetric unimodal maps with non-universal period-doubling scaling laws, Communications in Mathematical Physics 379, 1 (2020), 103−143. Article MathSciNet

2019

Davoud Cheraghi, Typical orbits of quadratic polynomials with a neutral fixed point: non-Brjuno type, Annales Scientifiques de l'École Normale Supérieure. Quatrième Série 52, 1 (2019), 59−138. MathSciNet Preprint
Matteo Tanzi, Tiago Pereira, and Sebastian van Strien, Robustness of ergodic properties of non-autonomous piecewise expanding maps, Ergodic Theory and Dynamical Systems 39, 4 (2019), 1121−1152. Article MathSciNet

2018

Artur Avila and Davoud Cheraghi, Statistical properties of quadratic polynomials with a neutral fixed point, Journal of the European Mathematical Society (JEMS) 20, 8 (2018), 2005−2062. 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

Trevor Clark, Sebastian van Strien, and Sofia Trejo, Complex bounds for real maps, Communications in Mathematical Physics 355, 3 (2017), 1001−1119. Article MathSciNet Preprint

2016

Vyacheslav Z. Grines, Olga V. Pochinka, and Sebastian van Strien, On 2-diffeomorphisms with one-dimensional basic sets and a finite number of moduli, Moscow Mathematical Journal 16, 4 (2016), 727−749. Article MathSciNet

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
Davoud Cheraghi and Arnaud Chéritat, A proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type, Inventiones Mathematicae 202, 2 (2015), 677−742. 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
Weixiao Shen and Sebastian van Strien, Recent developments in interval dynamics, in: Proceedings of the International Congress of Mathematicians Seoul 2014, Volume III, 699−719, Kyung Moon Sa, Seoul, 2014. MathSciNet Preprint
Sebastian van Strien, Milnor's conjecture on monotonicity of topological entropy: results and questions, in: Frontiers in complex dynamics, Princeton Mathematical Series, 323−337, Princeton University Press, Princeton, New Jersey, 2014. MathSciNet

2013

Henk Bruin and Sebastian van Strien, On the structure of isentropes of polynomial maps, Dynamical Systems 28, 3 (2013), 381−392. Article MathSciNet
Davoud Cheraghi, Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type, Communications in Mathematical Physics 322, 3 (2013), 999−1035. Article MathSciNet
Julian Newman, Regularization of a disk in a frictionable wedge, in: Mathematical Modelling (Inge Troch and Felix Breitenecker), 830−835, Vienna University of Technology, Vienna, 2013. Article
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
Gerson Florence, Tiago Pereira, and Jürgen Kurths, Extracellular potassium dynamics in the hyperexcitable state of the neuronal ictal activity, Communications in Nonlinear Science and Numerical Simulation 17, 12 (2012), 4700−4706. 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
Lasse Rempe and Sebastian van Strien, Absence of line fields and Mañé's theorem for nonrecurrent transcendental functions, Transactions of the American Mathematical Society 363, 1 (2011), 203−228. 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

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
Sebastian van Strien, One-parameter families of smooth interval maps: density of hyperbolicity and robust chaos, Proceedings of the American Mathematical Society 138, 12 (2010), 4443−4446. Article MathSciNet
Sebastian van Strien, One-dimensional dynamics in the new millennium, Discrete and Continuous Dynamical Systems A 27, 2 (2010), 557−588. Article MathSciNet

2009

Vítor Araújo, Stefano Luzzatto, and Marcelo Viana, Invariant measures for interval maps with critical points and singularities, Advances in Mathematics 221, 5 (2009), 1428−1444. Article MathSciNet
Katie Bloor and Stefano Luzzatto, Some remarks on the geometry of the standard map, International Journal of Bifurcation and Chaos 19, 7 (2009), 2213−2232. Article MathSciNet
Oleg Kozlovski and Sebastian van Strien, Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials, Proceedings of the London Mathematical Society 99, 2 (2009), 275−296. Article MathSciNet
Christian Pötzsche and Martin Rasmussen, Hibernation prevents chaos: a logistic case study, in: Difference equations and applications (M. Bohner, Z. Doslá, G. Ladas, M. Ünal, A. Zafer), 259−274, Uğur-Bahçeşehir Univ. Publ. Co., Istanbul, 2009. MathSciNet

2008

Henk Bruin, Juan Rivera-Letelier, Weixiao Shen, and Sebastian van Strien, Large derivatives, backward contraction and invariant densities for interval maps, Inventiones Mathematicae 172, 3 (2008), 509−533. Article MathSciNet
Yongluo Cao, Stefano Luzzatto, and Isabel Rios, The boundary of hyperbolicity for Hénon-like families, Ergodic Theory and Dynamical Systems 28, 4 (2008), 1049−1080. Article MathSciNet
Sarah Day, Hiroshi Kokubu, Stefano Luzzatto, Konstantin Mischaikow, Hiroe Oka, and Paveł Pilarczyk, Quantitative hyperbolicity estimates in one-dimensional dynamics, Nonlinearity 21, 9 (2008), 1967−1987. Article MathSciNet

2007

Oliver Butterley and Carlangelo Liverani, Smooth Anosov flows: correlation spectra and stability, Journal of Modern Dynamics 1, 2 (2007), 301−322. Article MathSciNet
Arek Goetz, Sebastian van Strien, and Franco Vivaldi, Special issue on geometric dynamics with singularities, Dynamical Systems 22, 1 (2007), 1. Article MathSciNet
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
Oleg Kozlovski, Weixiao Shen, and Sebastian van Strien, Density of hyperbolicity in dimension one, Annals of Mathematics 166, 1 (2007), 145−182. Article MathSciNet
Oleg Kozlovski, Weixiao Shen, and Sebastian van Strien, Rigidity for real polynomials, Annals of Mathematics 165, 3 (2007), 749−841. Article MathSciNet
Tanya Schmah and Cristina Stoica, Saari's conjecture is true for generic vector fields, Transactions of the American Mathematical Society 359, 9 (2007), 4429−4448. Article MathSciNet
Sebastian van Strien and Edson Vargas, Erratum to: Real bounds, ergodicity and negative Schwarzian for multimodal maps, Journal of the American Mathematical Society 20, 1 (2007), 267−268. Article MathSciNet

2006

Henk Bruin and Stefano Luzzatto, Topological invariance of the sign of the Lyapunov exponents in one-dimensional maps, Proceedings of the American Mathematical Society 134, 1 (2006), 265−272. Article MathSciNet
Henk Bruin, Weixiao Shen, and Sebastian van Strien, Existence of unique SRB-measures is typical for real unicritical polynomial families, Annales Scientifiques de l'École Normale Supérieure. Quatrième Série 39, 3 (2006), 381−414. Article MathSciNet
Yongluo Cao, Stefano Luzzatto, and Isabel Rios, Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: horseshoes with internal tangencies, Discrete and Continuous Dynamical Systems A 15, 1 (2006), 61−71. Article MathSciNet
Karla Díaz-Ordaz, Decay of correlations for non-Hölder observables for one-dimensional expanding Lorenz-like maps, Discrete and Continuous Dynamical Systems A 15, 1 (2006), 159−176. Article MathSciNet
Karla Díaz-Ordaz, Mark P. Holland, and Stefano Luzzatto, Statistical properties of one-dimensional maps with critical points and singularities, Stochastics and Dynamics 6, 4 (2006), 423−458. 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
Mark P. Holland and Stefano Luzzatto, Stable manifolds under very weak hyperbolicity conditions, Journal of Differential Equations 221, 2 (2006), 444−469. Article MathSciNet
Tobias H. Jäger and Jaroslav Stark, Towards a classification for quasiperiodically forced circle homeomorphisms, Journal of the London Mathematical Society 73, 3 (2006), 727−744. Article MathSciNet
Stefano Luzzatto, Stochastic-like behaviour in nonuniformly expanding maps, in: Handbook of Dynamical Systems. Vol. 1B, 265−326, Elsevier, Amsterdam, 2006. Article MathSciNet
Stefano Luzzatto and Hiroki Takahasi, Computable conditions for the occurrence of non-uniform hyperbolicity in families of one-dimensional maps, Nonlinearity 19, 7 (2006), 1657−1695. Article MathSciNet
Stefano Luzzatto and Lanyu Wang, Topological invariance of generic non-uniformly expanding multimodal maps, Mathematical Research Letters 13, 2−3 (2006), 343−357. Article MathSciNet

2005

José F. Alves, Stefano Luzzatto, and Vilton Pinheiro, Markov structures and decay of correlations for non-uniformly expanding dynamical systems, Annales de l'Institut Henri Poincaré. Analyse Non Linéaire 22, 6 (2005), 817−839. Article MathSciNet
Mark P. Holland and Stefano Luzzatto, A new proof of the stable manifold theorem for hyperbolic fixed points on surfaces, Journal of Difference Equations and Applications 11, 6 (2005), 535−551. Article MathSciNet

2004

José F. Alves, Stefano Luzzatto, and Vilton Pinheiro, Lyapunov exponents and rates of mixing for one-dimensional maps, Ergodic Theory and Dynamical Systems 24, 3 (2004), 637−657. Article MathSciNet
Yongluo Cao, Stefano Luzzatto, and Isabel Rios, A minimum principle for Lyapunov exponents and a higher-dimensional version of a theorem of Ma\~né, Qualitative Theory of Dynamical Systems 5, 2 (2004), 261−273. Article MathSciNet
Sebastian van Strien and Edson Vargas, Real bounds, ergodicity and negative Schwarzian for multimodal maps, Journal of the American Mathematical Society 17, 4 (2004), 749−782 (electronic). Article MathSciNet

2003

José F. Alves, Stefano Luzzatto, and Vilton Pinheiro, Markov structures for non-uniformly expanding maps on compact manifolds in arbitrary dimension, Electronic Research Announcements of the American Mathematical Society 9(2003), 26−31. Article MathSciNet
Henk Bruin, Stefano Luzzatto, and Sebastian van Strien, Decay of correlations in one-dimensional dynamics, Annales Scientifiques de l'École Normale Supérieure. Quatrième Série 36, 4 (2003), 621−646. Article MathSciNet
Henk Bruin, Weixiao Shen, and Sebastian van Strien, Invariant measures exist without a growth condition, Communications in Mathematical Physics 241, 2−3 (2003), 287−306. MathSciNet
Henk Bruin and Sebastian van Strien, Expansion of derivatives in one-dimensional dynamics, Israel Journal of Mathematics 137(2003), 223−263. Article MathSciNet
Jaroslav Stark, Transitive sets for quasi-periodically forced monotone maps, Dynamical Systems 18, 4 (2003), 351−364. 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
Kevin N. Webster and John N. Elgin, Asymptotic analysis of the Michelson system, Nonlinearity 16, 6 (2003), 2149−2162. Article MathSciNet

2001

Henk Bruin and Sebastian van Strien, Existence of absolutely continuous invariant probability measures for multimodal maps, in: Global analysis of dynamical systems, 433−447, Inst. Phys., Bristol, 2001. MathSciNet

2000

Genadi Levin and Sebastian van Strien, Bounds for maps of an interval with one critical point of inflection type. II, Inventiones Mathematicae 141, 2 (2000), 399−465. Article MathSciNet
Genadi Levin and Sebastian van Strien, Total disconnectedness of Julia sets and absence of invariant linefields for real polynomials, Astérisque , 261 (2000), xii, 161−172. MathSciNet
Stefano Luzzatto, Bounded recurrence of critical points and Jakobson's theorem, in: The Mandelbrot set, theme and variations, London Mathematical Society Lecture Note Series, 173−210, Cambridge University Press, Cambridge, 2000. MathSciNet
Stefano Luzzatto and Marcelo Viana, Positive Lyapunov exponents for Lorenz-like families with criticalities, Astérisque , 261 (2000), 201−237. MathSciNet
Sebastian van Strien, Misiurewicz maps unfold generically (even if they are critically non-finite), Fundamenta Mathematicae 163, 1 (2000), 39−54. MathSciNet

1998

Genadi Levin and Sebastian van Strien, Local connectivity of the Julia set of real polynomials, Annals of Mathematics 147, 3 (1998), 471−541. Article MathSciNet

1996

Henk Bruin, Gerhard Keller, Tomasz Nowicki, and Sebastian van Strien, Wild Cantor attractors exist, Annals of Mathematics 143, 1 (1996), 97−130. Article MathSciNet
Roza Galeeva and Sebastian van Strien, Which families of l-modal maps are full?, Transactions of the American Mathematical Society 348, 8 (1996), 3215−3221. Article MathSciNet
Sebastian van Strien, Transitive maps which are not ergodic with respect to Lebesgue measure, Ergodic Theory and Dynamical Systems 16, 4 (1996), 833−848. Article MathSciNet

1995

Sebastian van Strien, Real bounds in complex dynamics, in: Real and complex dynamical systems, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 211−229, Kluwer Acad. Publ., Dordrecht, 1995. MathSciNet

1993

Welington de Melo and Sebastian van Strien, One-dimensional dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete 25, Springer, Berlin, 1993. MathSciNet

1992

Marco Martens, Welington de Melo, and Sebastian van Strien, Julia-Fatou-Sullivan theory for real one-dimensional dynamics, Acta Mathematica 168, 3−4 (1992), 273−318. Article MathSciNet

1991

Henk Broer, Freddy Dumortier, Sebastian van Strien, and Floris Takens, Structures in dynamics, Studies in Mathematical Physics 2, North-Holland Publishing Co., Amsterdam, 1991. MathSciNet
Tomasz Nowicki and Sebastian van Strien, Invariant measures exist under a summability condition for unimodal maps, Inventiones Mathematicae 105, 1 (1991), 123−136. Article MathSciNet

1990

Jean-Marc Gambaudo, Sebastian van Strien, and Charles Tresser, Vers un ordre de Sarkovskiĭ pour les plongements du disque préservant l'orientation, Comptes Rendus de l'Académie des Sciences. Série I. Mathématique 310, 5 (1990), 291−294. MathSciNet
Marco Martens, Sebastian van Strien, Welington de Melo, and Pedro Mendes, On Cherry flows, Ergodic Theory and Dynamical Systems 10, 3 (1990), 531−554. Article MathSciNet
Tomasz Nowicki and Sebastian van Strien, Nonhyperbolicity and invariant measures for unimodal maps, Annales de l'Institut Henri Poincaré. Physique Théorique 53, 4 (1990), 427−429. Article MathSciNet
Tomasz Nowicki and Sebastian van Strien, Hyperbolicity properties of C^2 multi-modal Collet-Eckmann maps without Schwarzian derivative assumptions, Transactions of the American Mathematical Society 321, 2 (1990), 793−810. Article MathSciNet
Sebastian van Strien, One-dimensional versus two-dimensional dynamics, in: Open problems in topology, 645−654, North-Holland, Amsterdam, 1990. MathSciNet
Sebastian van Strien, Hyperbolicity and invariant measures for general C^2 interval maps satisfying the Misiurewicz condition, Communications in Mathematical Physics 128, 3 (1990), 437−495. Article MathSciNet

1989

Welington de Melo and Sebastian van Strien, A structure theorem in one-dimensional dynamics, Annals of Mathematics 129, 3 (1989), 519−546. Article MathSciNet
Jean-Marc Gambaudo, Sebastian van Strien, and Charles Tresser, The periodic orbit structure of orientation preserving diffeomorphisms on D^2 with topological entropy zero, Annales de l'Institut Henri Poincaré. Physique Théorique 50, 3 (1989), 335−356. Article MathSciNet
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

1988

Welington de Melo and Sebastian van Strien, One-dimensional dynamics: the Schwarzian derivative and beyond, Bulletin of the American Mathematical Society 18, 2 (1988), 159−162. Article MathSciNet
Tomasz Nowicki and Sebastian van Strien, Absolutely continuous invariant measures for C^2 unimodal maps satisfying the Collet-Eckmann conditions, Inventiones Mathematicae 93, 3 (1988), 619−635. Article MathSciNet
Sebastian van Strien, Smooth dynamics on the interval (with an emphasis on quadratic-like maps), in: New directions in dynamical systems, London Math. Soc. Lecture Note Ser., 57−119, Cambridge Univ. Press, Cambridge, 1988. 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

1981

Sebastian van Strien, On the bifurcations creating horseshoes, in: Dynamical systems and turbulence, Lecture Notes in Mathematics, 316−351, Springer, Berlin, 1981. MathSciNet