| Full text | |
| Author(s): |
Rodriguez Hertz, F.
;
Rodriguez Hertz, M. A.
;
Tahzibi, A.
;
Ures, R.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Ergodic Theory and Dynamical Systems; v. 32, p. 15-pg., 2012-04-01. |
| Abstract | |
We obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of three-dimensional manifolds having compact center leaves: either there is a unique entropy-maximizing measure, this measure has the Bernoulli property and its center Lyapunov exponent is 0, or there are a finite number of entropy-maximizing measures, all of them with non-zero center Lyapunov exponents (at least one with a negative exponent and one with a positive exponent), that are finite extensions of a Bernoulli system. In the first case of the dichotomy, we obtain that the system is topologically conjugated to a rotation extension of a hyperbolic system. This implies that the second case of the dichotomy holds for an open and dense set of diffeomorphisms in the hypothesis of our result. As a consequence, we obtain an open set of topologically mixing diffeomorphisms having more than one entropy-maximizing measure. (AU) | |
| FAPESP's process: | 09/17136-7 - Entropy maximizing measures for partially hyperbolic diffeomorphisms |
| Grantee: | Ali Tahzibi |
| Support Opportunities: | Regular Research Grants |