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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.)

Unstable entropy of partially hyperbolic diffeomorphisms along non-compact subsets

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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 type: Regular Research Grants