标题： $k$型混沌的$\mathbb{Z}^d$动作 显示英文标题

标题： $k$-type chaos of $\mathbb{Z}^d$ actions

摘要： 在本文中，我们定义并研究了由紧致度量空间上的$\mathbb{Z}^d$作用给出的动力系统中的$k$类型邻近对、$k$类型渐近对和$k$类型Li Yorke敏感性概念。我们证明了$k$类型概念的Auslander-Yorke二分定理。还研究了这些概念在一致共轭下的保持性。我们还研究了这些概念与其在通常动力系统中的类似概念之间的关系。 显示英文摘要

摘要： In this paper, we define and study the notions of $k$-type proximal pairs, $k$-type asymptotic pairs and $k$-type Li Yorke sensitivity for dynamical systems given by $\mathbb{Z}^d$ actions on compact metric spaces. We prove the Auslander-Yorke dichotomy theorem for $k$-type notions. The preservation of some of these notions under uniform conjugacy is also studied. We also study relations between these notions and their analogous notions in the usual dynamical systems.