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The entropy of an extended map for abelian group actions

Yuan Lian

Abstract

In this paper, we mainly consider on the entropy of the extended map conditional to the natural extension of a dynamical system for an Abelian group action and we calculate the entropy is zero.

The entropy of an extended map for abelian group actions

Abstract

In this paper, we mainly consider on the entropy of the extended map conditional to the natural extension of a dynamical system for an Abelian group action and we calculate the entropy is zero.
Paper Structure (3 sections, 3 theorems, 27 equations)

This paper contains 3 sections, 3 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Extension
  3. Main result

Key Result

Theorem 1.1

(DZ) Let $(Y, \mathcal{D}, \nu, G)$ be an MDS, $\mathcal{W}\in C_{Y}$ and $\mathcal{C} \subseteq \mathcal{D}$ a $G$-invariant sub-$\sigma$-algebra. Assume that $(Y,\mathcal{D}, \nu)$ is a Lebesgue space. Then

Theorems & Definitions (5)

  • Theorem 1.1
  • Proposition 1.1
  • proof
  • Theorem 3.1
  • proof