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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On the Bernoulli property for certain partially hyperbolic diffeomorphisms

Full text
Author(s):
Ponce, G. [1] ; Tahzibi, A. [2] ; Varao, R. [1]
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: 12/14620-8 - Fine ergodic properties of partially hyperbolic dynamical systems
Grantee:Gabriel Ponce
Support type: Scholarships abroad - Research Internship - Doctorate (Direct)
FAPESP's process: 15/02731-8 - Rigidity of partially hyperbolic dynamical systems and Anosov systems
Grantee:Gabriel Ponce
Support type: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 16/22475-9 - Different contexts for chaos
Grantee:José Régis Azevedo Varão Filho
Support type: Regular Research Grants
FAPESP's process: 17/06463-3 - Probabilistic and algebraic aspects of smooth dynamical systems
Grantee:Ali Tahzibi
Support type: Research Projects - Thematic Grants
FAPESP's process: 16/05384-0 - Dynamics of foliations and rigidity of ergodic measures
Grantee:Gabriel Ponce
Support type: Regular Research Grants
FAPESP's process: 14/23485-2 - Partially hyperbolic diffeomorphisms: Lyapunov exponents and equilibrium states
Grantee:Ali Tahzibi
Support type: Scholarships abroad - Research
FAPESP's process: 09/16792-8 - Fine ergodic properties of partially hyperbolic systems
Grantee:Gabriel Ponce
Support type: Scholarships in Brazil - Doctorate (Direct)
FAPESP's process: 11/21214-3 - Absolute continuity of the central foliation for partially hyperbolic systems
Grantee:José Régis Azevedo Varão Filho
Support type: Scholarships in Brazil - Post-Doctorate