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On non-chaotic hyperbolic sets

Noriaki Kawaguchi

Abstract

We give necessary and sufficient conditions for a hyperbolic set to be non-chaotic (or, conversely, chaotic) in a certain sense.

On non-chaotic hyperbolic sets

Abstract

We give necessary and sufficient conditions for a hyperbolic set to be non-chaotic (or, conversely, chaotic) in a certain sense.
Paper Structure (2 sections, 16 theorems, 60 equations)

This paper contains 2 sections, 16 theorems, 60 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem 1.2

Key Result

Lemma 1.1

For any expansive homeomorphism $f\colon X\to X$, the following conditions are equivalent

Theorems & Definitions (33)

  • Definition 1.1
  • Lemma 1.1
  • Lemma
  • Lemma 1.2
  • proof
  • Theorem 1.1
  • Remark 1.1
  • Definition 1.2
  • Definition 1.3
  • Definition 1.4
  • ...and 23 more