Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Weyl mean equicontinuity and Weyl mean sensitivity of a random dynamical system

Yuan Lian

Abstract

In this article, we introduce the concepts of Weyl mean equicontinuity and Weyl mean sensitivity of a random dynamical system associated to an infinite countable discrete amenable group action. We obtain the dichotomy result to Weyl mean equicontinuity and Weyl mean sensitivity of a random dynamical system when the corresponding skew product transformation is minimal and Ωis finite.

Weyl mean equicontinuity and Weyl mean sensitivity of a random dynamical system

Abstract

In this article, we introduce the concepts of Weyl mean equicontinuity and Weyl mean sensitivity of a random dynamical system associated to an infinite countable discrete amenable group action. We obtain the dichotomy result to Weyl mean equicontinuity and Weyl mean sensitivity of a random dynamical system when the corresponding skew product transformation is minimal and Ωis finite.
Paper Structure (5 sections, 9 theorems, 59 equations)

This paper contains 5 sections, 9 theorems, 59 equations.

Table of Contents

  1. introduction
  2. Preliminaries
  3. Besicovitch-,Weyl-,and Banach- mean equicontinuity for RDS
  4. Weyl-mean sensitivity for RDS
  5. Main result

Key Result

Theorem 3.8

Let $G$ be a countable amenable group, $(\Omega,\mathcal{F},\mathbb{P},G)$ a MDS and is continuous random dynamical system. Then

Theorems & Definitions (24)

  • Definition 2.1
  • Definition 3.1
  • Definition 3.2
  • Definition 3.4
  • Definition 3.5
  • Theorem 3.8
  • proof
  • Remark 3.9
  • Corollary 3.10
  • Definition 3.11
  • ...and 14 more