曲面上动力学的同位素稳定性

摘要：

本文研究了可定向曲面的保向同胚类中在合痕下持续存在的动力学。研究了周期点关于周期和强Nielsen等价的持久性。证明了关于这些关系的动态极小表示的存在性，并给出了等价类的合痕稳定性的充要条件。它还表明，大多数的最小的代表性的动力学坚持在同位素的意义上，任何同位素地图有一个不变的集合，这是它的共轭。

英文摘要：

This paper investigates dynamics that persist under isotopy in classes of orientation-preserving homeomorphisms of orientable surfaces. The persistence of periodic points with respect to periodic and strong Nielsen equivalence is studied. The existence of a dynamically minimal representative with respect to these relations is proved and necessary and sufficient conditions for the isotopy stability of an equivalence class are given. It is also shown that most the dynamics of the minimal representative persist under isotopy in the sense that any isotopic map has an invariant set that is semiconjugate to it.

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