逆极限空间上移位映射的拓扑熵与混沌

逆极限空间上移位映射的拓扑熵与混沌 TOPOLOGICAL ENTROPY AND CHAOS OF SHIFT MAPS ON THE INVERSE LIMIT SPACES 顾荣宝 Gu Rongbao 1 first-author 武汉大学数学系 武汉大学数学系 Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 研究了紧致度量空间上连续映射ｆ：Ｘ→Ｘ的逆极限空间上移位映射σｆ：ｌｉｍ（Ｘ，ｆ）→ｌｉｍ（Ｘ，ｆ）的拓扑熵与Ｌｉ－Ｙｏｒｋｅ意义下的混沌．证明了１)ｈ（σｆ）＝ｈ（ｆ）；２)ｆ为满射时，σｆ是Ｌｉ－Ｙｏｒｋｅ意义下混沌的当且仅当ｆ是Ｌｉ－Ｙｏｒｋｅ意义下混沌的． We prove the results alout the shift map on the inverse limit space of a compact metric space and a sole bonding map: 1) The topological entropy of the shift map is equal to the topologlcal entropy of the sole bonding map; 2) The shift map is chaotic in the sense of Li and Yorke if f its sole bonding map is chaotic in the sense of Li and Yorke. 逆极限空间 移位映射 拓扑熵 Li－Yorke混沌 inverse limit space shift map topological entropy chaotic in the sense of Li and Yorke O189.1 1995-01-01 2021-04-01 1