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Tiago Pereira
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Fabrizio Bianchi
Trevor Clark
Alexandre De Zotti
Gabriel Fuhrmann
Nikos Karaliolios
Dongchen Li
Sina Türeli
Björn Winckler
Sajjad Bakrani Balani
Giulia Carigi
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Wei Hao Tey
Kalle Timperi
Mike Field
Shangzhi Li
Ole Peters
Camille Poignard
Cristina Sargent
Bill Speares
Sofia Trejo Abad
Mauricio Barahona
Davoud Cheraghi
Martin Hairer
Darryl Holm
Xue-Mei Li
Greg Pavliotis


Sebastian van Strien

Chair in Dynamical Systems


Phone: +44(207)59-42844
Room: 6M36 Huxley Building

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Publications Sebastian van Strien since 1996 (by date)


with Trevor Clark, Quasisymmetric rigidity in one-dimensional dynamics, https://arxiv.org/abs/1805.09284. Submitted for publication. 143 pages.

with Trevor Cark and Edson de Faria, Dynamics of asymptotically holomorphic polynomial-like maps, https://arxiv.org/abs/1804.06122, Submitted for publication. 47 pages.


with Viacheslav Grines and Olga Pochinka, A complete topological classification of Morse-Smale diffeomorphisms on surfaces: a kind of kneading theory in dimension two, http://arxiv.org/abs/1712.02230

with Tiago Pereira and Matteo Tanzi, Heterogeneously Coupled Maps: hub dynamics and emergence across connectivity layers, https://arxiv.org/abs/1704.06163. To appear in J. Eur. Math. Soc.

with Trevor Clark and Sofia Trejo, Complex box bounds for real maps, arXiv:1310.8338v3. Updated version. Commun. Math Phys. 355 (2017), no 3, 1001-1119.


with Genadi Levin and Weixiao Shen, Transversality for critical relations of families of rational maps: an elementary proof , arXiv.org/abs/1702.02582

with Genadi Levin and Weixiao Shen, Monotonicity of entropy and positively oriented transversality for families of interval maps, arXiv.org/abs/1611.10056

with Matteo Tanzi and Tiago Pereira, Robustness of ergodic properties of nonautonomous piecewise expanding maps. arXiv.org/abs/1611.04016. To appear in ETDS.

with Viacheslav Grines and Olga Pochinka, On 2-diffeomorphisms with one-dimensional basic sets and a finite number of moduli, arXiv.org/abs/1608.00439. Moscow Mathematical Journal. 2016. Vol. 16. No. 4. 727-749.


with Lasse Rempe, Density of hyperbolicity for classes of real transcendental entire functions and circle maps, Duke Math. J. 164 (2015), no. 6, 1079–1137.

with Henk Bruin, Monotonicity of entropy for real multimodal maps, Journal of the AMS. 28 (2015), 1-61.


with Trevor Clark, Quasi-symmetric rigidity of real analytic and C^3 one-dimensional maps. Manuscript.

with Weixiao Shen, Recent developments in interval dynamics. Proceedings of the International Congress of Mathematicians, Seoul 2014, 699-719.

with Georg Ostrovski, Payoff performance of fictitious play, Journal of Dynamics and Games 1 (2014), 621-638.

Milnor's Conjecture on Monotonicity of Topological Entropy: results and questions. in "Frontiers in Complex Dynamics:In Celebration of John Milnor's 80th Birthday", Editor(s): Bonifant, Lyubich, Sutherland, Princeton University Press, ISBN:9780691159294, (2014), 323-337.


with Trevor Clark and Sofia Trejo, Complex box bounds for real maps, arXiv:1310.8338. Submitted for publication

with Tiago Pereira and Jeroen Lamb, Dynamics of expanding maps in heterogeneous networks, arXiv:1308.5526. Submitted for publication.

with Henk Bruin, On the structure of isentropes of polynomial maps, Dynamical Systems: An International Journal 28 (2013), 381-392


with Weixiao Shen, On stochastic stability of expanding circle maps with neutral fixed points, Dynamical Systems: An International Journal 28 (2013), 423-452.


with Colin Sparrow, Fictitious Play in 3x3 Games: chaos and dithering behaviour, Games and Economic Behavior 73 (2011), 262-286. Some of the computations were done by Maple, and can be downloaded. Maple worksheet 1 computation for first piece of orbit; Maple worksheet 2 second piece of orbit; Maple worksheet 3 computation of ratios

with Alexandre Eremenko, Rational functions with real multipliers, Trans. AMS 363 (2011), 6453-6463

with Colin Sparrow, Dynamics associated to games (fictitious play) with chaotic behavior, in "Dynamics, Games and Science I", Editors Peixoto, Pinto and Rand. Springer Verlag 2011.

with Georg Ostrovski, Piecewise Linear Hamiltonian Flows Associated to Zero-Sum Games: Transition Combinatorics and Questions on Ergodicity. Published in Regular and Chaotic Dynamics, 16, 1-2, (2011), 129-154.

Hamiltonian flows with random-walk behavior originating from zero-sum games and fictitious play, Nonlinearity 24 (2011), 1715-1742.

with Lasse Rempe, Absence of line fields and Mañé's theorem for non-recurrent transcendental functions, Trans. Amer. Math. Soc. 363 (2011) 203-228


One-dimensional dynamics in the new millennium, Discrete and Continuous Dynamical Systems 27 (2010), 557-588.

One-Parameter Families of Smooth Interval Maps: Density of Hyperbolicity and Robust Chaos, Proc. AMS 138 (2010), 4443-4446.


with Oleg Kozlovski,Stable maps are dense in dimension one . In: Sidoravicius, Vladas (ed.), New trends in mathematical physics. Selected contributions of the XVth international congress on mathematical physics, Rio de Janeiro, Brazil, August 5--11, 2006. Dordrecht: Springer. 403-412 (2009). MSC2000:

with Oleg Kozlovski, Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials, Proceedings of the LMS (2) 99 (2009), 275--296.


with Colin Sparrow and Christopher Harris, Fictitious Play in 3x3 Games: the transition between periodic and chaotic bahavior. Games and Economic Behavior 63, (2008), 259-291. Download maple worksheet clockwise orbit and maple worksheet anticlockwise orbit

Henk Bruin, Juan Rivera-Letelier, Weixiao Shen and Sebastian van Strien, Large derivatives, backward contraction and invariant densities for interval maps,   Inventiones Math. 172, (2008), 509-533.


Oleg Kozlovski, Weixiao Shen and Sebastian van Strien, Rigidity for real polynomials. Annals of Mathematics 165 (May 2007), 749-841.

Oleg Kozlovski, Weixiao Shen and Sebastian van Strien, Density of hyperbolicity in dimension one. Annals of Mathematics 166 (July 2007), 145-182.


Henk Bruin, Weixiao Shen and Sebastian van Strien, Existence of unique SRB-measures is typical for unimodal families, Annales Scientifiques de l'ENS (4) 39 (2006), no 4, 381--414

O. Kozlovski, P. Pintus, S. van Strien and R. de Vilder, Business-cycle models and the dangers of linearizing, Journal of Optimization Theory and Applications, 128 (2006), 333-353.


Sebastian van Strien and Edson Vargas, Real Bounds, ergodicity and negative Schwarzian for multimodal maps J. Amer. Math. Soc. 17 (2004), 749-782.


Henk Bruin, Weixiao Shen and Sebastian van Strien, Invariant measures exist without a growth condition, Commun. Math. Phys. 241 (2003), 287-306.

Henk Bruin, Stefano Luzzatto and Sebastian van Strien, Decay of correlations in one-dimensional dynamics. Annales Scientifiques de l'École Norm. Sup. (4) 36 (2003), no. 4, 621--646.

Henk Bruin and Sebastian van Strien, Expansion of Derivatives in One-Dimensional Dynamics, Israel Journal of Mathematics, 137 (2003), 223-263.


Henk Bruin and Sebastian van Strien, Existence of acips for multimodal maps , in `Global analysis of dynamical systems, Festschrift dedicated to Floris Takens for this 60th birthday', Edited by H.W. Broer, B. Krauskopf and G. Vegter, IOP (2001), 433-447.


S. van Strien, Misiurewicz maps unfold generically, Fundamenta Mathematica 163 (2000), 39-54.

G. Levin and S. van Strien, Bounds for maps of an interval with one critical point of inflection type, Inventiones Mathematicae, 141 (2000), 399--465.

G. Levin and S. van Strien, Total disconnectedness of Julia sets and absense of invariant linefields for real polynomials, Asterisque, 261 (2000), 161-172.


O. Kozlovski, S. van Strien and R. de Vilder, The two-fixed point lemma, Preprint November 1999


G. Levin and S. van Strien, Local connectivity of the Julia set of real polynomials, Annals of Math., 147 (1998), 471-541.


H. Bruin, G. Keller, T. Nowicki and S. van Strien, Wild Cantor attractors exist, Annals of Math., 143 (1996), 97-130

R. Galeeva, S. van Strien, Which families of $l$-modal maps are full? Trans. of the A.M.S., 348 (1996), 3215-3221.

S. van Strien,Transitive Maps which are not Ergodic with respect to Lebesgue Measure. Ergod. Theory and Dynam. Syst., 16 (1996), 833-848


S. van Strien, Real bounds in complex dynamics, Appeared in `Real and complex Dynamical Systems', edited by B. Branner and P. Hjorth, published by Kluwer Academic Publishers, Series: C: Mathematical and Physical Sciences - Vol. 464, (1995)