Weak Horseshoe with Bounded-Gap-Hitting Times

Abstract

In this paper, we consider weak horseshoe with bounded-gap-hitting times. For a flow $(M,\phi )$, it is shown that if the time one map $(M,\phi _1)$ has weak horseshoe with bounded-gap-hitting times, so is $(M,\phi _\tau )$ for all $\tau \ne 0$. In addition, we prove that for an affine homeomorphism of a compact metric abelian group, positive topological entropy is equivalent to weak horseshoe with bounded-gap-hitting times.

Keywords

Weak Horseshoe / Entropy / Hitting times / Semi-Horseshoe / Flow