动力系统对称性的反转与扩展
A brief guide to reversing and extended symmetries of dynamical systems
摘要：
反向对称群是动力系统对称群的一个很好的研究扩展，后者由拓扑空间上的单个同胚的作用定义。虽然它传统上被认为是在非线性动力学，其中空间是简单的，但地图是复杂的，它有一个有趣的对应符号动力学，其中地图是简单的，但空间不是。此外，在高维移位的情况下有一个有趣的扩展，其中类似的概念可以通过移位空间的全自同构群中作用群的中心化子和规范化子引入。我们回顾基本概念，并回顾一些已知的结果，在一个相当非正式的方式，给第一印象的现象，可以出现在从中心化的扩展到规范化，一些强调最近的发展。
英文摘要：
The reversing symmetry group is a well-studied extension of the symmetry group of a dynamical system, the latter being defined by the action of a single homeomorphism on a topological space. While it is traditionally considered in nonlinear dynamics, where the space is simple but the map is complicated, it has an interesting counterpart in symbolic dynamics, where the map is simple but the space is not. Moreover, there is an interesting extension to the case of higher-dimensional shifts, where a similar concept can be introduced via the centraliser and the normaliser of the acting group in the full automorphism group of the shift space. We recall the basic notions and review some of the known results, in a fairly informal manner, to give a first impression of the phenomena that can show up in the extension from the centraliser to the normaliser, with some emphasis on recent developments.
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