Uniform hyperbolic approximations of measures with non-zero Lyapunov exponents

Autor:	Fernando José Sánchez-Salas, Stefano Luzzatto
Rok vydání:	2013
Předmět:	Discrete mathematics Pure mathematics Hyperbolic secant distribution Applied Mathematics General Mathematics Hyperbolic manifold Lyapunov exponent Riemannian manifold Relatively hyperbolic group Stable manifold symbols.namesake symbols Ergodic theory Mathematics Hyperbolic equilibrium point
Zdroj:	Proceedings of the American Mathematical Society. 141:3157-3169
ISSN:	1088-6826 0002-9939
DOI:	10.1090/s0002-9939-2013-11565-0
Popis:	We show that for any C 1 + α C^{1+\alpha } diffeomorphism of a compact Riemannian manifold, every non-atomic, ergodic, invariant probability measure with non-zero Lyapunov exponents is approximated by uniformly hyperbolic sets in the sense that there exists a sequence Ω n \Omega _{n} of compact, topologically transitive, locally maximal, uniformly hyperbolic sets such that for any sequence { μ n } \{\mu _{n}\} of f f -invariant ergodic probability measures with s u p p ( μ n ) ⊆ Ω n supp (\mu _{n}) \subseteq \Omega _{n} we have μ n → μ \mu _{n}\to \mu in the weak- ∗ * topology.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8acd37ea827107b5c0ec9ff8a1511ee5 https://doi.org/10.1090/s0002-9939-2013-11565-0 Zobrazit plný text záznamu