Recurrence and Higher Ergodic Properties for Quenched Random Lorentz Tubes in Dimension Bigger than Two

Marcello Seri, Marco Lenci*, Mirko degli Esposti, Giampaolo Cristadoro

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
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Abstract

We consider the billiard dynamics in a non-compact set of a"e (d) that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

Original languageEnglish
Pages (from-to)124-138
Number of pages15
JournalJournal of Statistical Physics
Volume144
Issue number1
DOIs
Publication statusPublished - Jul-2011
Externally publishedYes

Keywords

  • Hyperbolic billiards
  • Lorentz gas
  • Infinite-measure dynamical systems
  • Infinite ergodic theory
  • Random environment
  • Channel
  • Tube
  • SEMI-DISPERSING BILLIARDS
  • FUNDAMENTAL THEOREM
  • METALLIC BODIES
  • HYPERBOLICITY
  • MOTION
  • GAS

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