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。