Regular and Chaotic Dynamics

, Volume 12, Issue 3, pp 335–356 | Cite as

Regularity of Bunimovich’s stadia

  • N. Chernov
  • H. -K. Zhang
Research Articles

Abstract

Stadia are popular models of chaotic billiards introduced by Bunimovich in 1974. They are analogous to dispersing billiards due to Sinai, but their fundamental technical characteristics are quite different. Recently many new results were obtained for various chaotic billiards, including sharp bounds on correlations and probabilistic limit theorems, and these results require new, more powerful technical apparatus. We present that apparatus here, in the context of stadia, and prove “regularity” properties.

Keywords

billiards stadium hyperbolicity chaos absolute continuity distortion bounds 

MSC2000 numbers

37J35 37J30 70H06 22E10 

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Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • N. Chernov
    • 1
  • H. -K. Zhang
    • 1
  1. 1.Department of MathematicsUniversity of Alabama at BirmingharnUSA

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