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Low-dimensional dynamical systems
Preprints
- 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
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