Robust existence of nonhyperbolic ergodic measures with positive entropy and full support

Autor: Christian Bonatti, Lorenzo J. Díaz, Dominik Kwietniak

Publikováno v: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore 2021, 22 (4), pp.1643-1672. ⟨10.2422/2036-2145.202001_014⟩

We prove that for some manifolds $M$ the set of robustly transitive partially hyperbolic diffeomorphisms of $M$ with one-dimensional nonhyperbolic centre direction contains a $C^1$-open and dense subset of diffeomorphisms with nonhyperbolic measures

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::62ddf962eb01bb97493302361811d3c3
https://hal.science/hal-03860928

Weak* and entropy approximation of nonhyperbolic measures: a geometrical approach

Autor: Lorenzo J. Díaz, Bruno Santiago, Katrin Gelfert

Publikováno v: Mathematical Proceedings of the Cambridge Philosophical Society. 169:507-545

We study $C^1$-robustly transitive and nonhyperbolic diffeomorphisms having a partially hyperbolic splitting with one-dimensional central bundle whose strong un-/stable foliations are both minimal. {In dimension $3$, an important class of examples of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e6f310fe813ef3e6368a9c76c43ba47a
https://doi.org/10.1017/s0305004119000276

Topological and ergodic aspects of partially hyperbolic diffeomorphisms and nonhyperbolic step skew products

Autor: Lorenzo J. Díaz, Katrin Gelfert, M. Rams

Publikováno v: Proceedings of the Steklov Institute of Mathematics. 297:98-115

We review some ergodic and topological aspects of robustly transitive partially hyperbolic diffeomorphisms with one-dimensional center direction. We also discuss step skew-product maps whose fiber maps are defined on the circle which model such dynam

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::937246011b61b173dbe4b9538c2ebdcc
https://doi.org/10.1134/s008154381704006x

Blender-horseshoes in Center-unstable Hénon-like Families

Autor: Sebastián A. Pérez, Lorenzo J. Díaz

Publikováno v: New Trends in One-Dimensional Dynamics ISBN: 9783030168322

A blender-horseshoe is a locally maximal transitive hyperbolic set that appears in dimension at least three carrying a distinctive geometrical property: its local stable manifold “behaves” as a manifold of topological dimension greater than the e

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::511b6f7643b0c5d51c95e3d1b4e810c3
https://doi.org/10.1007/978-3-030-16833-9_8

A criterion for zero averages and full support of ergodic measures

Autor: Christian Bonatti, Jairo Bochi, Lorenzo J. Díaz

Publikováno v: Moscow Mathematical Journal
Moscow Mathematical Journal, Independent University of Moscow 2018, 18 (1), pp.15-61
Moscow mathematical journal
Moscow mathematical journal, 2018, 18 (1), pp.15-61. 〈http://www.mathjournals.org/mmj/2018-018-001/2018-018-001-002.html〉
Artículos CONICYT
CONICYT Chile
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International audience; Consider a homeomorphism $f$ defined on a compact metric space $X$ and a continuous map $\phi\colon X \to \mathbb{R}$. We provide an abstract criterion, called control at any scale with a long sparse tail for a point $x\in X$

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2b927d11190762e3e940704a9bca35b1
https://hal.archives-ouvertes.fr/hal-01758598