| Full text | |
| Author(s): |
Ponce, Gabriel
Total Authors: 1
|
| Document type: | Journal article |
| Source: | Nonlinearity; v. 32, n. 7, p. 2337-2351, JUL 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
Given a partially hyperbolic diffeomorphism f : M -> M defined on a compact Riemannian manifold M, in this paper we define the concept of unstable topological entropy off on a set Y subset of M not necessarily compact. Using recent results of Yang (2016 (arXiv:1601.05504)) and Hu et al (2017 Adv. Math. 321 31-68) we extend a theorem of Bowen (1973 Trans. Am. Math. Soc. 184 125-36) proving that, for an ergodic f-invariant measure it , the unstable measure theoretical entropy off is upper bounded by the unstable topological entropy off on any set of positive mu-measure. We define a notion of unstable topological entropy of f using a Hausdorff dimension like characterization and we prove that this definition coincides with the definition of unstable topological entropy introduced in Hu et al (2017 Adv. Math. 321 31-68). (AU) | |
| FAPESP's process: | 16/05384-0 - Dynamics of Foliations and Rigidity of Ergodic Measures |
| Grantee: | Gabriel Ponce |
| Support Opportunities: | Regular Research Grants |