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Focusing Components in Typical Chaotic Billiards Should be Absolutely Focusing

  • Leonid A. Bunimovich
  • Alexander GrigoEmail author
Article

Abstract

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.

Keywords

Boundary Component Nonlinear Stability Stable Periodic Orbit Billiard Table Birkhoff Normal Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.ABC Math ProgramGeorgia Institute of TechnologyAtlantaU.S.A
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaU.S.A.

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