| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Univ Estadual Campinas, IMECC, Dept Matemat, Campinas, SP - Brazil
[2] Univ Sao Paulo, ICMC, Dept Matemat, Sao Carlos, SP - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | ADVANCES IN MATHEMATICS; v. 329, p. 329-360, APR 30 2018. |
| Web of Science Citations: | 1 |
| Abstract | |
We address the classical problem of equivalence between Kolmogorov and Bernoulli property of smooth dynamical systems. In a natural class of volume preserving partially hyperbolic diffeomorphisms homotopic to Anosov ({''}derived from Anosov{''}) on 3-torus, we prove that Kolmogorov and Bernoulli properties are equivalent. In our approach, we propose to study the conditional measures of volume along central foliation to recover fine ergodic properties for partially hyperbolic diffeomorphisms. As an important consequence we obtain that there exists an almost everywhere conjugacy between any volume preserving derived from Anosov diffeomorphism of 3-torus and its linearization. Our results also hold in higher dimensional case when central bundle is one dimensional and stable and unstable foliations are quasi-isometric. (C) 2018 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 09/16792-8 - Fine ergodic properties of partially hyperbolic systems |
| Grantee: | Gabriel Ponce |
| Support Opportunities: | Scholarships in Brazil - Doctorate (Direct) |
| FAPESP's process: | 15/02731-8 - Rigidity of partially hyperbolic dynamical systems and Anosov systems |
| Grantee: | Gabriel Ponce |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 11/21214-3 - Absolute continuity of the central foliation for partially hyperbolic systems |
| Grantee: | José Régis Azevedo Varão Filho |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 16/05384-0 - Dynamics of Foliations and Rigidity of Ergodic Measures |
| Grantee: | Gabriel Ponce |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 14/23485-2 - Partially hyperbolic diffeomorphisms: Lyapunov exponents and equilibrium states |
| Grantee: | Ali Tahzibi |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 12/14620-8 - Fine ergodic properties of partially hyperbolic dynamical systems |
| Grantee: | Gabriel Ponce |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate (Direct) |
| FAPESP's process: | 17/06463-3 - Probabilistic and algebraic aspects of smooth dynamical systems |
| Grantee: | Ali Tahzibi |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 16/22475-9 - Different contexts for chaos |
| Grantee: | José Régis Azevedo Varão Filho |
| Support Opportunities: | Regular Research Grants |