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.
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页码：2479 / 2490
页数：12
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