Conditions Implying Annular Chaos: Quantitative results and Computer Assisted Proofs
Dynamical Systems
2025-06-10 v1
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.
Keywords
Cite
@article{arxiv.2506.06608,
title = {Conditions Implying Annular Chaos: Quantitative results and Computer Assisted Proofs},
author = {M. J. Capiński and M. Gröger and A. Passeggi and F. A. Tal},
journal= {arXiv preprint arXiv:2506.06608},
year = {2025}
}