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Weak Horseshoe with Bounded-Gap-Hitting Times
Communications in Mathematics and Statistics ( IF 1.1 ) Pub Date : 2020-06-03 , DOI: 10.1007/s40304-020-00209-4
Leiye Xu , Junren Zheng

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.



中文翻译:

有限的击球时间的弱马蹄

在本文中,我们考虑了具有有限间隙击中时间的弱马蹄形。对于流\((M,\ phi)\),表明如果时间一幅地图\((M,\ phi _1)\)的马蹄形具有有限的缺口击中时间,那么\(( M,\ phi _ \ tau)\)所有\(\ tau \ ne 0 \)。此外,我们证明了对于一个紧凑的度量阿贝尔群的仿射同胚性,正拓扑熵等效于具有有限间隙击中时间的弱马蹄形。

更新日期:2020-07-24
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