On the number of ergodic physical/SRB measures of singular-hyperbolic attracting sets

Autor:	Araujo, Vitor
Rok vydání:	2022
Předmět:	Mathematics - Dynamical Systems 37D25 (Primary) 37D30 37D20 (Secondary)
Zdroj:	Journal of Differential Equations Volume 354, 5 (2023):373-402
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jde.2023.02.008
Popis:	It is known that sectional-hyperbolic attracting sets, for a $C^2$ flow on a finite dimensional compact manifold, have at most finitely many ergodic physical invariant probability measures. We prove an upper bound for the number of distinct ergodic physical measures supported on a connected singular-hyperbolic attracting set for a $3$-flow. This bound depends only on the number of Lorenz-like equilibria contained in the attracting set. Examples of singular-hyperbolic attracting sets are provided showing that the bound is sharp. Comment: 31 pages, 13 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.10084 Zobrazit plný text záznamu View this record from Arxiv