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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: badaolong@sina.com)
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Abstract

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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.

Information

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

References

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