A class of differentiable toral maps which are topologically mixing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

按检索

A class of differentiable toral maps which are topologically mixing

Authors:	Naoya Sumi

Institution:	Department of Mathematics, Tokyo Metropolitan University, Tokyo 192-03, Japan

Abstract:	We show that on the 2-torus $\mathbb{T}^{2}$ there exists a $C^{1}$ open set $\mathcal{U}$ of $C^{1}$ regular maps such that every map belonging to $\mathcal{U}$ is topologically mixing but is not Anosov. It was shown by Mañé that this property fails for the class of $C^{1}$ toral diffeomorphisms, but that the property does hold for the class of $C^{1}$ diffeomorphisms on the 3-torus $\mathbb{T}^{3}$ . Recently Bonatti and Diaz proved that the second result of Mañé is also true for the class of $C^{1}$ diffeomorphisms on the -torus $\mathbb{T}^{n}$ ( $n\ge 4$ ).

Keywords:	Anosov differentiable map DA-map sensitive dependence on initial conditions topological mixing transversal homoclinic point

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文