Typical Recurrence for the Ehrenfest Wind-Tree Model

2010/04/20 by Serge Troubetzkoy · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Finite set #Hyperboloid model #Lorentz covariance #Lorentz transformation #Mathematical Dynamics and Fractals #Navier-Stokes equation solutions #Sense (electronics) #Set (abstract data type) #math.DS

paper · pdf · doi:10.1007/s10955-010-0026-5

published as Journal of Statistical Physics (2010) 60-67

arxiv created 2010/04/20 · openalex publication_date 2010/08/16 · arxiv updated 2012/01/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show that the typical wind-tree model, in the sense of Baire, is recurrent and has a dense set of periodic orbits. The recurrence result also holds for the Lorentz gas : the typical Lorentz gas, in the sense of Baire, is recurrent. These Lorentz gases need not be of finite horizon!

Citations

• Aperiodic Lorentz gas: recurrence and ergodicity
• Typicality of recurrence for Lorentz gases
• The nonequilibrium Ehrenfest gas: A chaotic model with flat obstacles?

Cited by

• Infinite-horizon Lorentz tubes and gases: Recurrence and ergodic properties
• Recurrence in generic staircases