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arXiv · 1307.3817

On multi-transitivity with respect to a vector

Zhijing Chen·Jian Li·Jie Lü
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Abstract

A topological dynamical system $(X,f)$ is said to be multi-transitive if for every $n\in\mathbb{N}$ the system $(X^{n}, f\times f^{2}\times \dotsb\times f^{n})$ 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 [On weak mixing, minimality and weak disjointness of all iterates, Erg. Th. Dynam. Syst., 32 (2012), 1661--1672]. We also show that multi-transitive systems are Li-Yorke chaotic.

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Zhijing Chen, Jian Li, Jie Lü. 2013-07-15. On multi-transitivity with respect to a vector. https://doi.org/10.1007/s11425-014-4797-z

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