文献类型：期刊文献

英文题名：Characterizing ergodicity of induced hyperspace dynamical systems

作者：Li, Risong[1]

机构：[1]Guangdong Ocean Univ, Sch Math & Comp Sci, Zhanjiang 524025, Peoples R China

年份：2020

卷号：26

期号：1

起止页码：223

外文期刊名：BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA

收录：ESCI(收录号：WOS:000525932000014)、Scopus(收录号：2-s2.0-85059870609)、WOS

基金：The author thanks the referees very much for many valuable comments and suggestions which greatly improved the writing of the paper. This research was supported the Opening Project of Artificial Intelligence Key Laboratory of Sichuan Province (2018RZJ03), the Opening Project of Bridge Non-destruction Detecting and Engineering Computing Key Laboratory of Sichuan Province (2018QZJ03) and the Key Scientific and Technological Research Project of Science and Technology Department of Zhanjiang City (Grant 2010C3112005).

语种：英文

外文关键词：Topological (c-)ergodicity; Topological (c-)strong ergodicity; Topological (c-)transitivity; Hyperspace dynamical system; Hit-or-miss topology

外文摘要：Let E be Hausdorff locally compact second countable spaces (HLCSC) and (2E,2f) (hit-or-miss topology equipped) be hyperspace dynamical system induced by a given dynamical system (E, f). In this paper, the concepts of topologically co-compact ergodicity (resp. topologically co-compact strong ergodicity) and topologically co-compact double ergodicity (resp. topologically co-compact double strong ergodicity) are introduced for dynamical systems. For any HLCSC system (E, f), these three conditions on (E, f) are, respectively, equivalent to topological ergodicity (resp. topologically strong ergodicity) and topological double ergodicity (resp. topological double strong ergodicity) on (2E,2f). The concept of topologically co-compact exact (c-exact) is also introduced, and we show that if f is perfect and c-exact, then 2f:F00 -> F00 is topologically exact, where F00={F is an element of F0:. In addition, other noticeable properties of topologically co-compact ergodicity (resp. topologically co-compact strong ergodicity) and topologically co-compact double ergodicity (resp. topologically co-compact double strong ergodicity) are studied.