In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation betw...In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation between local measure-theoretic polynomial entropy of Borel probability measures and polynomial entropy on an arbitrary subset. Also, we establish a variational principle for polynomial entropy on compact subsets in the context of amenable group actions.展开更多
In this article,we showed that positive relative entropy implies mean Li-Yorke chaos along some good sequences in the fiber.Our result extended Li and Qiao’s result in[Monatsh.Math.,186(2018),153-173].
基金supported by Foundation in higher education institutions of He’nan Province,P. R. China(Grant No. 23A110020)National Natural Science Foundation of China (Grant No. 11401363)+4 种基金the Foundation for the Training of Young Key Teachers in Colleges and Universities in He’nan Province,P. R. China (Grant No.2018GGJS134)supported by National Natural Science Foundation of China (Gratn No.11971236)China Postdoctoral Science Foundation (Grant No. 2016M591873)China Postdoctoral Science Special Foundation (Grant No. 2017T100384)funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation between local measure-theoretic polynomial entropy of Borel probability measures and polynomial entropy on an arbitrary subset. Also, we establish a variational principle for polynomial entropy on compact subsets in the context of amenable group actions.
基金Supported by National Natural Science Foundation of China(Grant Nos.12071222,11971236)China Postdoctoral Science Foundation(Grant No.2016M591873)China Postdoctoral Science Special Foundation(Grant No.2017T100384)。
文摘In this article,we showed that positive relative entropy implies mean Li-Yorke chaos along some good sequences in the fiber.Our result extended Li and Qiao’s result in[Monatsh.Math.,186(2018),153-173].
