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Positively n-expansive homeomorphisms and the L-shadowing property

Bernardo Carvalho, Welington Cordeiro

Abstract

We discuss further the dynamics of n-expansive homeomorphisms with the shadowing property, started in [7]. The L-shadowing property is defined and the dynamics of n-expansive homeomorphisms with such property is explored. In particular, we prove that positively n-expansive homeomorphisms with the L-shadowing property can only be defined in finite metric spaces.

Positively n-expansive homeomorphisms and the L-shadowing property

Abstract

We discuss further the dynamics of n-expansive homeomorphisms with the shadowing property, started in [7]. The L-shadowing property is defined and the dynamics of n-expansive homeomorphisms with such property is explored. In particular, we prove that positively n-expansive homeomorphisms with the L-shadowing property can only be defined in finite metric spaces.

Paper Structure

This paper contains 4 sections, 9 theorems, 43 equations.

Table of Contents

  1. Introduction and statement of results
  2. Positively $N$-expansive homeomorphisms
  3. The L-shadowing property
  4. Acknowledgments

Key Result

Theorem A

If a positively $n$-expansive homeomorphism is defined in a compact metric space $X$ and has the L-shadowing property, then $X$ is finite.

Theorems & Definitions (17)

  • Definition 1
  • Definition 2
  • Theorem A
  • Theorem B
  • Theorem C
  • Definition 3
  • Theorem 2.1
  • Proposition 1
  • proof
  • Lemma 2.2
  • ...and 7 more