Fundamental domain of invariant sets and applications

Abstract

Let $X$ be a compact metric space and $f:X\to X$ a homeomorphism on $X$. We construct a fundamental domain for the set with finite peaks for each cocycle induced by $\varphi \in C(X,R)$. In particular we prove that if a partially hyperbolic diffeomorphism is accessible, then either the set with finite peaks for the Jacobian cocycle is of full volume, or the set of transitive points is of positive volume.

References in corpus (1)

• Partially hyperbolic sets with positive measure and $ACIP$ for partially hyperbolic systems