Conjugacy classes of real analytic one-dimensional maps are analytic connected manifolds
T Clark, S van Strien - arXiv preprint arXiv:2304.00883, 2023 - arxiv.org
An important question is to describe topological conjugacy classes of dynamical systems.
Here we show that within the space of real analytic one-dimensional maps with critical …
Here we show that within the space of real analytic one-dimensional maps with critical …
Asymptotically holomorphic methods for infinitely renormalizable unimodal maps
T Clark, E De Faria, S Van Strien - Ergodic Theory and Dynamical …, 2023 - cambridge.org
The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically
holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of …
holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of …
Quasisymmetric rigidity in one-dimensional dynamics
T Clark, S van Strien - arXiv preprint arXiv:1805.09284, 2018 - arxiv.org
In the late 1980's Sullivan initiated a programme to prove quasisymmetric rigidity in one-
dimensional dynamics: interval or circle maps that are topologically conjugate are …
dimensional dynamics: interval or circle maps that are topologically conjugate are …
The Full Renormalization Horseshoe for Real Box Maps With Minimal Post-Critical Sets
Y Wang - International Mathematics Research Notices, 2024 - academic.oup.com
In this paper, we consider the renormalization operator for real box maps with minimal post-
critical sets. We show the existence of the full renormalization horseshoe for real box maps …
critical sets. We show the existence of the full renormalization horseshoe for real box maps …
[PDF][PDF] Dennis Sullivan's Work on Dynamics
E de Faria, S van Strien - arXiv preprint arXiv:2306.06290, 2023 - arxiv.org
arXiv:2306.06290v1 [math.DS] 9 Jun 2023 Page 1 Dennis Sullivan’s Work on Dynamics Edson
de Faria and Sebastian van Strien Before going into Dennis Sullivan’s work on dynamics, we …
de Faria and Sebastian van Strien Before going into Dennis Sullivan’s work on dynamics, we …
Asymmetric unimodal maps with non-universal period-doubling scaling laws
O Kozlovski, S van Strien - Communications in Mathematical Physics, 2020 - Springer
We consider a family of strongly-asymmetric unimodal maps {f_t\} _ t ∈ 0, 1 ft t∈ 0, 1 of the
form f_t= t ⋅ f ft= t· f where f: 0, 1 → 0, 1 f: 0, 1→ 0, 1 is unimodal, f (0)= f (1)= 0 f (0)= f (1)= 0, f …
form f_t= t ⋅ f ft= t· f where f: 0, 1 → 0, 1 f: 0, 1→ 0, 1 is unimodal, f (0)= f (1)= 0 f (0)= f (1)= 0, f …
Dennis Sullivan's Work on Dynamics
Abstract Before going into Dennis Sullivan's work on dynamics, we would like to share some
of our reminiscences on the remarkable way in which he influenced a huge number of …
of our reminiscences on the remarkable way in which he influenced a huge number of …
The boundary of chaos for interval mappings
T Clark, S Trejo - Proceedings of the London Mathematical …, 2020 - Wiley Online Library
A goal in the study of dynamics on the interval is to understand the transition to positive
topological entropy. There is a conjecture from the 1980s that the only route to positive …
topological entropy. There is a conjecture from the 1980s that the only route to positive …
Dynamics of asymptotically holomorphic polynomial-like maps
T Clark, E de Faria, S van Strien - arXiv preprint arXiv:1804.06122, 2018 - arxiv.org
The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically
holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of …
holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of …
Shy shadows of infinite-dimensional partially hyperbolic invariant sets
D Smania - Ergodic Theory and Dynamical Systems, 2019 - cambridge.org
Shy shadows of infinite-dimensional partially hyperbolic invariant sets Page 1 Ergod. Th. &
Dynam. Sys. (2019), 39, 1361–1400 doi:10.1017/etds.2017.65 c Cambridge University Press …
Dynam. Sys. (2019), 39, 1361–1400 doi:10.1017/etds.2017.65 c Cambridge University Press …