Unstable entropy of partially hyperbolic diffeomorphisms along non-compact subsets

Abstract

Given a partially hyperbolic diffeomorphism $f:M\to M$ 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 $\mu$, the unstable measure theoretical entropy of $f$ is upper bounded by the unstable topological entropy of $f$ on any set of full $\mu$-measure. We also define a notion of unstable topological entropy of $f$ using a Hausdorff dimension like characterization.

Cited by in corpus (1)

• Unstable entropy in smooth ergodic theory