| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, ICMC, Dept Matemat, BR-13566590 Sao Carlos, SP - Brazil
[2] Univ Fed Fluminense, Inst Matemat & Estat, Dept Geometria, BR-24020140 Niteroi, RJ - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 371, n. 2, p. 1231-1251, JAN 15 2019. |
| Web of Science Citations: | 4 |
| Abstract | |
A deep analysis of the Lyapunov exponents for stationary sequence of matrices going back to Furstenberg, for more general linear cocycles by Ledrappier, and generalized to the context of non-linear cocycles by Avila and Viana, gives an invariance principle for invariant measures with vanishing central exponents. In this paper, we give a new criterium formulated in terms of entropy for the invariance principle and, in particular, obtain a simpler proof for some of the known invariance principle results. As a byproduct, we study ergodic measures of partially hyperbolic diffeomorphisms whose center foliation is one-dimensional and forms a circle bundle. We show that for any such C-2 diffeomorphism which is accessible, weak hyperbolicity of ergodic measures of high entropy implies that the system itself is of rotation type. (AU) | |
| FAPESP's process: | 14/23485-2 - Partially hyperbolic diffeomorphisms: Lyapunov exponents and equilibrium states |
| Grantee: | Ali Tahzibi |
| Support Opportunities: | Scholarships abroad - Research |