A. Passeggi | Searcharxiv

arXiv2025

Conditions Implying Annular Chaos: Quantitative results and Computer Assisted Proofs

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.

math.DS↗

arXiv2020

Generic Rotation Sets in Hyperbolic Surfaces

We show that for generic homeomorphisms homotopic to the identity in a closed and oriented surface of genus $g>1$, the rotation set is given by a union of at most $2^{5g-3}$ convex sets. Examples showing the sharpness for this asymptotic order are provided.

math.DS↗