Topological entropy is not lower semi-continuous: small perturbation of the dynamical system can lead to a collapse of entropy. In this note we show that for some special classes of dynamical systems (geodesic flows, Reeb flows, positive contactomorphisms) topological entropy at least is stable in the sense that there exists a nontrivial continuous lower bound, given that a certain homological invariant grows exponentially.

中文翻译：

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接触同胚拓扑熵的 C0 稳定性

拓扑熵不是下半连续的：动力系统的小扰动会导致熵的崩溃。在本文中，我们展示了对于某些特殊类别的动力系统（测地线流、Reeb 流、正接触同构），鉴于某个同调不变量呈指数增长，拓扑熵至少在存在非平凡连续下界的意义上是稳定的。