Some sufficient conditions for transitivity of Anosov diffeomorphisms

Autor:	Micena, F.
Rok vydání:	2022
Předmět:	Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	Given a $C^2$- Anosov diffemorphism $f: M \rightarrow M,$ we prove that the jacobian condition $Jf^n(p) = 1,$ for every point $p$ such that $f^n(p) = p,$ implies transitivity. As application in the celebrated theory of Sinai-Ruelle-Bowen, this result allows us to state a classical theorem of Livsic-Sinai without directly assuming transitivity as a general hypothesis. A special consequence of our result is that every $C^2$-Anosov diffeomorphism, for which every point is regular, is indeed transitive. Comment: Manuscript submited for publication. It is a more lucid and clear part of arXiv:2011.06196
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.08930 Zobrazit plný text záznamu View this record from Arxiv