A Franks' lemma for convex planar billiards

被引：2

作者：

Visscher, Daniel ^{[1
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL | 2015年 / 30卷 / 03期

基金：

美国国家科学基金会;

关键词：

convex billiards; Franks' lemma; perturbation; linear Poincare map; POSITIVE TOPOLOGICAL-ENTROPY; GEODESIC-FLOWS; HYPERBOLICITY;

D O I：

10.1080/14689367.2015.1046815

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let. be an orbit of the billiard flow on a convex planar billiard table; then the perpendicular part of the derivative of the billiard flow along. is a symplectic linear map DP. This paper contains a proof of the following Franks' lemma for a residual set of convex planar billiard tables: for any closed orbit, the map DP can be perturbed freely within a neighbourhood in Sp(1) by a C-2-small perturbation in the space of convex planar billiard tables.

引用

页码：333 / 340

页数：8

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