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Topological entropy is generically infinite for non-Lipschitz velocity fields

Carl Johan Peter Johansson, Giulia Mescolini

Abstract

We prove that for any Osgood non-Lipschitz modulus of continuity $ω$, flow maps associated with time-periodic $ω$-continuous velocity fields generically (in the sense of Baire) have infinite topological entropy.

Topological entropy is generically infinite for non-Lipschitz velocity fields

Abstract

We prove that for any Osgood non-Lipschitz modulus of continuity , flow maps associated with time-periodic -continuous velocity fields generically (in the sense of Baire) have infinite topological entropy.

Paper Structure

This paper contains 5 sections, 33 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Notation
  3. Topological entropy
  4. Entropy-increasing building block
  5. Proof of Theorem \ref{['thm:main']}

Figures (1)

  • Figure 1: Comparison of subsets before and after transformation $T$ with $N=4$.

Theorems & Definitions (16)

  • Remark 1.2
  • Remark 1.3
  • Remark 1.4
  • proof
  • Claim 3.2
  • proof : Proof of Claim
  • Example 3.3
  • Example 3.4
  • proof : Proof of Lemma \ref{['lemma:aux']}
  • Claim 4.2
  • ...and 6 more