On multi-transitivity with respect to a vector

Abstract

A topological dynamical system $(X,f)$ is said to be multi-transitive if for every $n\in \mathbb{N}$ the system $(X^n,f\times f^2\times \cdots \times f^n)$ 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.

11 pages

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