Dominated splitting from constant periodic data and global rigidity of Anosov automorphisms

Autor:	DeWitt, Jonathan, Gogolev, Andrey
Rok vydání:	2023
Předmět:	Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	We show that a $\mathrm{GL}(d,\mathbb{R})$ cocycle over a hyperbolic system with constant periodic data has a dominated splitting whenever the periodic data indicates it should. This implies global periodic data rigidity of generic Anosov automorphisms of $\mathbb{T}^d$. Further, our approach also works when the periodic data is narrow, that is, sufficiently close to constant. We can show global periodic data rigidity for certain non-linear Anosov diffeomorphisms in a neighborhood of an irreducible Anosov automorphism with simple spectrum. Comment: 25 pages; improvements to the exposition
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.07323 Zobrazit plný text záznamu View this record from Arxiv