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On multi-transitivity with respect to a vector |
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| Authors: | ZhiJing Chen Jian Li Jie Lü |
| Affiliation: | 1. Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China 2. Department of Mathematics, Shantou University, Shantou, 515063, China 3. School of Mathematics, South China Normal University, Guangzhou, 510631, China |
| Abstract: | A topological dynamical system (X, f) is said to be multi-transitive if for every n ∈ ? the system (X n , f × f 2 × … × f n ) is transitive. We introduce the concept of multi-transitivity with respect to a vector and show that multi-transitivity can be characterized by the hitting time sets of open sets, answering a question proposed by Kwietniak and Oprocha (2012). We also show that multi-transitive systems are Li-Yorke chaotic. |
| Keywords: | multi-transitivity weak mixing Furstenberg family Li-Yorke chaos |
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