Conditions Implying Annular Chaos: Quantitative results and Computer Assisted Proofs

TL;DR

This paper establishes quantitative conditions for chaos and diffusion in annular maps, and demonstrates their effectiveness through computer-assisted proofs across various classical and varied settings.

Contribution

It introduces easily implementable criteria for chaos in annular homeomorphisms and validates them with computer-assisted proofs for multiple classical families.

Findings

Proved chaos and diffusion in classical annular maps

Validated the criteria with computer-assisted proofs

Applicable to both conservative and dissipative systems

Abstract

We derive quantitative sufficient conditions for rotational chaos and diffusion in annular homeomorphisms, building on the topological criteria established in [31]. These conditions depend only on basic properties of the maps, making their implementation straightforward. To demonstrate the effectiveness of the method, we provide computer-assisted proofs of rotational chaos and diffusion for classical families of annular maps and their variations, in both conservative (twist and non-twist) and dissipative settings.