Topological entropy is generically infinite for non-Lipschitz velocity fields

TL;DR

This paper proves that for a broad class of non-Lipschitz velocity fields, the associated flow maps typically exhibit infinite topological entropy, indicating highly complex dynamics.

Contribution

It establishes that generic flow maps for time-periodic non-Lipschitz velocity fields have infinite topological entropy, extending understanding of chaotic behavior in such systems.

Findings

Flow maps with non-Lipschitz velocity fields are generically of infinite topological entropy.

The result applies to velocity fields with any Osgood non-Lipschitz modulus of continuity.

Infinite topological entropy indicates highly complex and chaotic dynamics.

Abstract

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