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On Moser’s boundedness problem of dual Billiards

Published online by Cambridge University Press:  01 April 2009

LONG LI
LONG LI*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China (email: [email protected])
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Abstract

In this paper, the boundedness of the dual billiard orbits of trapezoids is obtained. This gives an example showing that there are also polygons, which are neither rational nor quasi-rational, with all of their dual billiard orbits bounded. Moreover, most of the orbits are Poisson-stable, which means that most points will come sufficiently near to their original positions under iterations of the dual billiard map.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 2 , April 2009 , pp. 613 - 635
Copyright
Copyright © Cambridge University Press 2009

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