Focusing Components in Typical Chaotic Billiards Should be Absolutely Focusing

We demonstrate that the defocusing mechanism fails to work if not all focusing components of the boundary are absolutely focusing. More precisely, we construct billiard tables with arbitrary long free path away from a non-absolutely focusing component such that a nonlinearly stable periodic orbit ex...

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Bibliographic Details
Published in:	Communications in mathematical physics Vol. 293; no. 1; pp. 127 - 143
Main Authors:	Bunimovich, Leonid A., Grigo, Alexander
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer-Verlag 01-01-2010
Subjects:	Classical and Quantum Gravitation Complex Systems Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical Stable Periodic Orbit Billiard Table Nonlinear Stability Boundary Component Birkhoff Normal Form
Online Access:	Get full text
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Summary:	We demonstrate that the defocusing mechanism fails to work if not all focusing components of the boundary are absolutely focusing. More precisely, we construct billiard tables with arbitrary long free path away from a non-absolutely focusing component such that a nonlinearly stable periodic orbit exists. Therefore the only known standard procedure of constructing chaotic ergodic billiards works in general only if all focusing boundary components are absolutely focusing.
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-009-0927-9