Dispersing Billiards with Moving Scatterers

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• 作者：Mikko Stenlund (1) (2)
  Lai-Sang Young (3)
  Hongkun Zhang (4)
  
• 刊名：Communications in Mathematical Physics
• 出版年：2013
• 出版时间：September 2013
• 年：2013
• 卷：322
• 期：3
• 页码：909-955
• 全文大小：721KB
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• 作者单位：Mikko Stenlund (1) (2)
  Lai-Sang Young (3)
  Hongkun Zhang (4)
  
  1. Department of Mathematics, University of Rome 鈥淭or Vergata鈥? Via della Ricerca Scientifica, 00133, Roma, Italy
  2. Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, Helsinki, 00014, Finland
  3. Courant Institute of Mathematical Sciences, New York, NY, 10012, USA
  4. Department of Mathematics & Statistics, University of Massachusetts, Amherst, 01003, USA
  

文摘

We propose a model of Sinai billiards with moving scatterers, in which the locations and shapes of the scatterers may change by small amounts between collisions. Our main result is the exponential loss of memory of initial data at uniform rates, and our proof consists of a coupling argument for non-stationary compositions of maps similar to classical billiard maps. This can be seen as a prototypical result on the statistical properties of time-dependent dynamical systems.