Diffeomorphisms approximated by Anosov on the 2-torus and their SBR measures期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Diffeomorphisms approximated by Anosov on the 2-torus and their SBR measures

Authors:	Naoya Sumi

Affiliation:	Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-03, Japan

Abstract:	We consider the $C^{2}$ set of $C^{2}$ diffeomorphisms of the 2-torus $mathbb{T}^{2}$ , provided the conditions that the tangent bundle splits into the directed sum $Tmathbb{T}^{2}=E^{s}oplus E^{u}$ of -invariant subbundles $E^{s}$ , $E^{u}$ and there is such that $Vert Df\|_{E^{s}}Vert <lambda$ and $Vert Df\|_{E^{u}}Vert ge 1$ . Then we prove that the set is the union of Anosov diffeomorphisms and diffeomorphisms approximated by Anosov, and moreover every diffeomorphism approximated by Anosov in the $C^{2}$ set has no SBR measures. This is related to a result of Hu-Young.

Keywords:	Anosov diffeomorphism SBR measure

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