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arXiv · 1808.07131

Unstable entropy of partially hyperbolic diffeomorphisms along non-compact subsets

Gabriel Ponce
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Abstract

Given a partially hyperbolic diffeomorphism $f:M \rightarrow M$ defined on a compact Riemannian manifold $M$, in this paper we define the concept of unstable topological entropy of $f$ on a set $Y \subset M$ not necessarily compact and we extend a theorem of R. Bowen proving that, for an ergodic $f$-invariant measure $μ$, the unstable measure theoretical entropy of $f$ is upper bounded by the unstable topological entropy of $f$ on any set of full $μ$-measure. We also define a notion of unstable topological entropy of $f$ using a Hausdorff dimension like characterization.

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Gabriel Ponce. 2019-07-11. Unstable entropy of partially hyperbolic diffeomorphisms along non-compact subsets. https://doi.org/10.1088/1361-6544%2Fab1ba3

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