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Billiards on almost integrable polyhedral surfaces

Published online by Cambridge University Press:  19 September 2008

E. Gutkin
E. Gutkin
Affiliation:
Columbia University, New York, USA and Max-Planck-Institute für Mathematik, Bonn, West Germany†
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Abstract

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The phase space of the geodesic flow on an almost integrable polyhedral surface is foliated into a one-parameter family of invariant surfaces. The flow on a typical invariant surface is minimal. We associate with an almost integrable polyhedral surface its holonomy group which is a subgroup of the group of motions of the Euclidean plane. We show that if the holonomy group is discrete then the flow on an invariant surface is ergodic if and only if it is minimal.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 4 , December 1984 , pp. 569 - 584
Copyright
Copyright © Cambridge University Press 1984

References

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