arXiv subjects

Sebastián Pavez-Molina

Publications and source records attributed to Sebastián Pavez-Molina.

2 recordsLinked to original sources

arXiv2026

Local smooth rigidity of Anosov diffeomorphisms in $\mathbb{T}^{3}$

Given a $C^0$ conjugacy between two Anosov diffeomorphisms, the matching periodic data problem asks whether this conjugacy is smooth provided spectral data of the diffeomorphisms match at periodic points. We show that if the two $C^0$ conjugate diffeomorphisms on $\mathbb{T}^3$ are sufficiently close to a hyperbolic linear automorphism with a pair of complex conjugate eigenvalues, then the conjugacy must be smooth. In particular, we have that in a neighborhood of a hyperbolic toral automorphism, matching periodic data implies that the conjugacy is $C^{1+\text{Hölder}}$

math.DS↗

arXiv2020

Generic Rotation Sets

Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb{R}^{d})$ called a potential we define its rotation set $R(F)$ as the set of integrals of $F$ with respect to all $T$-invariant probability measures, which is a convex body of $\mathbb{R}^{d}$. In this paper, we study the geometry of rotation sets. We prove that if $T$ is a non-uniquely ergodic topological dynamical system with a dense set of periodic measures, then the map $R(\cdot)$ is open with respect to the uniform topologies. As a consequence, we obtain that the rotation set of a generic potential is strictly convex and has $C^{1}$ boundary. Furthermore, we prove that the map $R(\cdot)$ is surjective, extending a result of Kucherenko and Wolf.

math.DS↗