On uniformly quasiconformal Anosov diffeomorphisms with two dimensional distributions

We prove that a transitive uniformly $u$-quasiconformal Anosov diffeomorphism with a two-dimensional unstable distribution has a globally defined stable holonomy. As a corollary, we are able to remove an additional assumption in a theorem of Kalinin-Sadovskaya, and deduce that all transitive uniform...

Full description

Saved in:
Bibliographic Details
Main Author Zhang, Jiesong
Format Journal Article
LanguageEnglish
Published 31.10.2023
Subjects
Mathematics - Dynamical Systems
Online AccessGet full text

Cover

More Information
Summary:We prove that a transitive uniformly $u$-quasiconformal Anosov diffeomorphism with a two-dimensional unstable distribution has a globally defined stable holonomy. As a corollary, we are able to remove an additional assumption in a theorem of Kalinin-Sadovskaya, and deduce that all transitive uniformly quasiconformal Anosov diffeomorphisms are $C^{\infty}$-conjugate to affine Anosov diffeomorphisms on infra-torus.
DOI:10.48550/arxiv.2311.00251