集值离散动力系统的拓扑遍历性与链遍历性

Journal of Guangxi Normal University(Natural Science Edition) ›› 2011, Vol. 29 ›› Issue (1): 20-23.

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Topological Ergodicity and Chain Ergodicity of the Set-valuedDiscrete Dynamical Systems

MENG Xin, FAN Qin-jie, WANG Hong-ren

College of Jilin Normal University,Siping Jilin 136000,China

Received:2010-10-13 Published:2018-11-16

Abstract

Abstract: Let f:X→X and f be the set-valued mapwhich is induced by f .In the paper,it is proved that if f is topologically ergodic,it implies f is also topologically ergodic,the converse is not true,and the topological ergodicity of f and f is equilant under W^e-topology,then f is topologically ergodic if and only if f_mis topologically ergodic.It is also proved that,for some integerk,if f^k is chain ergodic,it implies f is also chain ergodic.Let f have POTP,7 equilant condtions on f which is chain ergodic are given.

Key words: set-valued maps, topological ergodicity, chain ergodicity

CLC Number:

O189.1

MENG Xin, FAN Qin-jie, WANG Hong-ren. Topological Ergodicity and Chain Ergodicity of the Set-valuedDiscrete Dynamical Systems[J].Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(1): 20-23.

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