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Regular and Chaotic Dynamics, 2007, Volume 12, Issue 3, Pages 335–356
DOI: https://doi.org/10.1134/S1560354707030057 (Mi rcd627) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Regularity of Bunimovich's Stadia

N. Chernova, H. K. Zhangb

a Department of Mathematics, University of Alabama at Birmingham, AL 35294, USA
b Department of Mathematics and Physics, North China Electric Power University, Baoding, Hebei 071003, China
Citations (4)
DOI: https://doi.org/10.1134/S1560354707030057
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.
Received: 03.03.2007
Accepted: 04.05.2007
Bibliographic databases:
Document Type: Article
MSC: 37J35, 37J30, 70H06, 22E10
Language: English
Citation: N. Chernov, H. K. Zhang, “Regularity of Bunimovich's Stadia”, Regul. Chaotic Dyn., 12:3 (2007), 335–356
Citation in format AMSBIB
\Bibitem{CheZha07}
\by N. Chernov, H.~K.~Zhang
\paper Regularity of Bunimovich's Stadia
\jour Regul. Chaotic Dyn.
\yr 2007
\vol 12
\issue 3
\pages 335--356
\mathnet{http://mi.mathnet.ru/rcd627}
\crossref{https://doi.org/10.1134/S1560354707030057}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2350328}
\zmath{https://zbmath.org/?q=an:1229.37031}
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  • https://www.mathnet.ru/eng/rcd627
  • https://www.mathnet.ru/eng/rcd/v12/i3/p335
    • This publication is cited in the following 4 articles:
    1. Wang F., Zhang H.-K., Zhang P., “Decay of Correlations For Unbounded Observables”, Nonlinearity, 34:4 (2021), 2402–2429  crossref  mathscinet  isi  scopus
    2. Mark F Demers, Hong-Kun Zhang, “Spectral analysis of hyperbolic systems with singularities”, Nonlinearity, 27:3 (2014), 379  crossref
    3. Péter Bálint, Miklós Halász, Jorge A Hernández-Tahuilán, David P Sanders, “Chaos and stability in a two-parameter family of convex billiard tables”, Nonlinearity, 24:5 (2011), 1499  crossref
    4. Nikolai Chernov, Hong-Kun Zhang, “On Statistical Properties of Hyperbolic Systems with Singularities”, J Stat Phys, 136:4 (2009), 615  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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