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

Autor: Christian Bonatti, Lorenzo J. Díaz, Dominik Kwietniak
Přispěvatelé: Bonatti, Christian, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Pontifical Catholic University of Rio de Janeiro (PUC), Faculty of Mathematics and Computer Science of the Jagiellonian University, Uniwersytet Jagielloński w Krakowie = Jagiellonian University (UJ), Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES)001CAPES-Ciencia sem fronteirasCNE-FaperjINCT/FAPERJE-16/2014CNPq-grants (Brazil)National Science Centre, Poland2013/08/A/ST1/00275Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES)88881.064927/2014-01ICERM-Brown University
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: 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⟩
ISSN: 0391-173X
2036-2145
DOI: 10.2422/2036-2145.202001_014⟩
Popis: 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 which are ergodic, fully supported and have positive entropy. To do so, we formulate abstract conditions sufficient for the construction of an ergodic, fully supported measure $\mu$ which has positive entropy and is such that for a continuous function $\phi\colon X\to\mathbb{R}$ the integral $\int\phi\,d\mu$ vanishes. The criterion is an extended version of the control at any scale with a long and sparse tail technique coming from the previous works.
Comment: 23 pages, 0 figures
Databáze: OpenAIRE
načítá se...