Complete regularity of linear cocycles and the Baire category of the set of Lyapunov-Perron regular points

Autor:	Bochi, Jairo, Pesin, Yakov, Sarig, Omri
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems 37D25 37D30
Druh dokumentu:	Working Paper
Popis:	Given a continuous linear cocycle $\mathcal{A}$ over a homeomorphism $f$ of a compact metric space $X$, we investigate its set $\mathcal{R}$ of Lyapunov-Perron regular points, that is, the collection of trajectories of $f$ that obey the conclusions of the Multiplicative Ergodic Theorem. We obtain results roughly saying that the set $\mathcal{R}$ is of first Baire category (i.e., meager) in $X$, unless some rigid structure is present. In some settings, this rigid structure forces the Lyapunov exponents to be defined everywhere and to be independent of the point; that is what we call complete regularity. Comment: 31 pages, no figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.01798 Zobrazit plný text záznamu View this record from Arxiv