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Related Experiment Videos

Cantori for the stadium billiard.

J. D. Meiss1

  • 1Program in Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526.

Chaos (Woodbury, N.Y.)
|April 1, 1992
PubMed
Summary

This study reveals that despite chaotic motion, regular orbits like periodic orbits and cantori exist in stadium billiards. These cantori act as barriers, hindering particle transport within the system.

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Area of Science:

  • Physics
  • Dynamical Systems
  • Mathematical Physics

Background:

  • Stadium billiards exhibit complex dynamics, with most orbits being chaotic.
  • However, regular orbits, including periodic and quasiperiodic ones, also exist within this system.
  • Understanding these regular structures is crucial for predicting particle transport.

Purpose of the Study:

  • To identify and characterize regular orbits, specifically periodic orbits and cantori, within the stadium billiard system.
  • To investigate the role of these regular orbits in influencing particle transport.

Main Methods:

  • Exploiting the symmetries of the stadium billiard to find specific types of periodic orbits (maximizing and saddle).
  • Analyzing the properties of cantori as quasiperiodic orbits with associated caustics.
  • Applying principles of dynamical systems and twist maps to understand transport phenomena.

Main Results:

  • Identified maximizing and saddle periodic orbits by leveraging stadium symmetries.
  • Characterized cantori as maximizing quasiperiodic orbits possessing caustics.
  • Demonstrated that cantori impede transport, especially for glancing orbits, consistent with twist map behavior.

Conclusions:

  • Regular orbits, including periodic orbits and cantori, are significant features within the stadium billiard dynamics.
  • Cantori play a critical role in hindering particle transport, impacting the overall system behavior.
  • The findings have implications for understanding transport in systems with mixed phase space.

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