Zobrazeno 1 - 10
of 504
pro vyhledávání: '"Pujals, Á."'
We formulate and prove $\textit{a priori}$ bounds for the renormalization of H\'enon-like maps (under certain regularity assumptions). This provides a certain uniform control on the small-scale geometry of the dynamics, and ensures pre-compactness of
Externí odkaz:
http://arxiv.org/abs/2411.13624
We carry out a detailed quantitative analysis on the geometry of invariant manifolds for smooth dissipative systems in dimension two. We begin by quantifying the regularity of any orbit (finite or infinite) in the phase space with a set of explicit i
Externí odkaz:
http://arxiv.org/abs/2411.13286
We introduce a class of infinitely renormalizable, unicritical diffeomorphisms of the disk (with a non-degenerate "critical point"). In this class of dynamical systems, we show that under renormalization, maps eventually become H\'enon-like, and then
Externí odkaz:
http://arxiv.org/abs/2401.13559
Autor:
Berger, Pierre, Bedford, Eric, Bianchi, Fabrizio, Buff, Xavier, Crovisier, Sylvain, Dinh, Tien-Cuong, Dujardin, Romain, Favre, Charles, Firsova, Tanya, Ingram, Patrick, Ishii, Yutaka, Palmisano, Liviana, Pujals, Enrique, Raissy, Jasmin, Štimac, Sonja, Vigny, Gabriel
We propose a set of questions on the dynamics of H\'enon maps from the real, complex, algebraic and arithmetic points of view.
Comment: 34 pages, 4 figures
Comment: 34 pages, 4 figures
Externí odkaz:
http://arxiv.org/abs/2312.03907
Autor:
Crovisier, Sylvain, Pujals, Enrique
Publikováno v:
Notices Amer. Math. Soc. 69 (2022), 748-761
In the sciences in general, the phrase "route to chaos" has come to refer to a metaphor when some physical, biological, economic, or social system transitions from one exhibiting order to one displaying randomness (or chaos). Sometimes the goal is to
Externí odkaz:
http://arxiv.org/abs/2302.05484
Autor:
Pujals, Sandra
Publikováno v:
Historia Mexicana, 2023 Jan 01. 723 (287), 1413-1456.
Externí odkaz:
https://www.jstor.org/stable/27181082
We show that robustly transitive endomorphisms of a closed manifolds must have a non-trivial dominated splitting or be a local diffeomorphism. This allows to get some topological obstructions for the existence of robustly transitive endomorphisms. To
Externí odkaz:
http://arxiv.org/abs/2106.03291
In the spirit of Kolmogorov typicality, we introduce the notion of germ-typicality: in a space of dynamics, it encompass all these phenomena that occur for a dense and open subset of parameters of any generic parametrized family of systems. For any $
Externí odkaz:
http://arxiv.org/abs/2103.16697
We discuss the dynamics of smooth diffeomorphisms of the disc with vanishing topological entropy which satisfy the mild dissipation property introduced in [CP]. In particular it contains the H\'enon maps with Jacobian up to 1/4. We prove that these s
Externí odkaz:
http://arxiv.org/abs/2005.14278
Autor:
Correa, Javier, Pujals, Enrique R.
We construct the complete set of orders of growth and we define on it the generalized entropy of a dynamical systems. With this object we provide a framework where we can study the separation of orbits of a map beyond the scope of exponential growth.
Externí odkaz:
http://arxiv.org/abs/2003.01257