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Projectional entropy for actions of amenable groups

Michał Prusik

Abstract

In the current paper we attempt to transfer the notion of the projectional entropy, originally defined for multidimensional subshifts, to the case of actions of amenable groups. The main theorem states that if a system is strongly irreducible the equality of the entropy and the projectional entropy implies that the system has a product-like structure.

Projectional entropy for actions of amenable groups

Abstract

In the current paper we attempt to transfer the notion of the projectional entropy, originally defined for multidimensional subshifts, to the case of actions of amenable groups. The main theorem states that if a system is strongly irreducible the equality of the entropy and the projectional entropy implies that the system has a product-like structure.
Paper Structure (3 sections, 12 theorems, 36 equations)

This paper contains 3 sections, 12 theorems, 36 equations.

Table of Contents

  1. Introduction
  2. Basic notions
  3. The results

Key Result

Lemma 2.2

Let $(F_n)$ be a Følner sequence in $G$ and let $B$ be a nonempty finite subset of $G$. Then $\tilde{F}_n:=BF_n$ is also a Følner sequence in $G$.

Theorems & Definitions (30)

  • Definition 2.1
  • Lemma 2.2
  • proof
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Theorem 2.7
  • Theorem 2.9
  • Theorem 2.10
  • Definition 3.1
  • ...and 20 more