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: |
Transitive relation
Pure mathematics Hyperbolicity Mathematics::Dynamical Systems Dense set Continuous function (set theory) [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS] Scale (descriptive set theory) Dynamical Systems (math.DS) Measure (mathematics) Theoretical Computer Science Positive entropy Mathematics (miscellaneous) FOS: Mathematics Ergodic theory 37D25 37D35 37D30 28D99 Mathematics - Dynamical Systems Mathematics Criterion |
| 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 |
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