Scarcity of Periodic Orbits in Outer Billiards

被引：0

作者：

Tumanov, Alexander ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, 1409 West Green St, Urbana, IL 61801 USA

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2020年 / 30卷 / 03期

关键词：

Outer billiard; Periodic orbit; Exterior differential system; SUB-RIEMANNIAN GEOMETRY; POINTS; SET;

D O I：

10.1007/s12220-017-9927-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a simple proof of the result of Tumanov and Zharnitsky (Int Math Res Not,2006) that the set of period 4 orbits in planar outer billiard with piecewise smooth convex boundary has empty interior, provided that no four corners of the boundary form a parallelogram. We also obtain results on period 5 and 6 orbits.

引用

页码：2479 / 2490

页数：12

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