常曲率曲面上的完全可积磁台球

Q3 Mathematics

Electronic Research Announcements in Mathematical Sciences Pub Date : 2012-08-12 DOI:10.3934/ERA.2012.19.112

M. Biały

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引用次数: 11

摘要

我们考虑在恒定磁场影响下，台球在恒定曲率曲面的凸域中的运动。证明了如果台球图是完全可积的，那么边界曲线必然是圆。这一结果表明，对于常曲率表面上的经典台球，最近得到的所谓Hopf刚性现象在恒磁场存在下也成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Totally integrable magnetic billiards on constant curvature surface

We consider billiard ball motion in a convex domain of a constant curvature surface influenced by the constant magnetic field. We prove that if the billiard map is totally integrable then the boundary curve is necessarily a circle. This result shows that the so-called Hopf rigidity phenomenon which was recently obtained for classical billiards on constant curvature surfaces holds true also in the presence of constant magnetic field.

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来源期刊

Electronic Research Announcements in Mathematical Sciences 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication. ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007