Weak Horseshoe with bounded-gap-hitting times

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.