Aperiodic Lorentz gas: recurrence and ergodicity

2002/06/27 by Marco Lenci, MARCO LENCI
Materials Science · Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Quasicrystal Structures and Properties #math-ph #math.DS #math.MP #msc:37A40 #msc:37D50 #nlin.CD

paper · pdf · doi:10.1017/s0143385702001529

published as Ergodic Theory Dynam. Systems 23 (2003), no. 3, 869-883 · 17 pages, 3 figures

arxiv created 2002/06/27 · openalex publication_date 2003/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that the general (i.e. possibly aperiodic) Lorenz gas in two dimensions, with finite horizon and non-degenerate geometrical features, is ergodic if it is recurrent. We also give examples of aperiodic recurrent gases.

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• The Lorenz Renormalization Conjecture
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• Measures with infinite Lyapunov exponents for the periodic Lorentz gas