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Polynomial entropy of induced homeomorphisms on $C(\mathbb{S}^1)$

Maša Đorić, Jelena Katić

Abstract

We compute the polynomial entropy of $C(f)$ where $f$ is any circle homeomorphism.

Polynomial entropy of induced homeomorphisms on $C(\mathbb{S}^1)$

Abstract

We compute the polynomial entropy of where is any circle homeomorphism.

Paper Structure

This paper contains 6 sections, 5 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Hyperspaces and induced maps
  4. Polynomial entropy
  5. Circle homeomorphisms
  6. Main results and proofs

Key Result

Theorem 1

(DK) Let $f:[0,1]\to [0,1]$ or $f:\mathbb{S}^1\to \mathbb{S}^1$ be a homeomorphism with a finite non-wandering set. Then $h_{\mathrm{pol}}(C(f))=2$, $h_{\mathrm{pol}}(F_n(f))=n$ and $h_{\mathrm{pol}}(2^{f})=\infty$.∎

Theorems & Definitions (5)

  • Theorem
  • Theorem 1
  • Lemma 2
  • Proposition 3
  • Proposition 4