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.
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页码：333 / 340
页数：8
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