2011/03/31 by Marco Lenci, Serge Troubetzkoy
Mathematics · Physics and Astronomy · #Aperiodic graph #Chaotic #Classical mechanics #Combinatorics #Computer science #Ergodic theory #Ergodicity #Geometry #Lorentz covariance #Lorentz transformation #Mathematical Dynamics and Fractals #Mathematics #Metric (unit) #Physics #Plane (geometry) #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Statistical physics #Stochastic processes and statistical mechanics #Uncountable set #math.DS
paper · pdf · doi:10.1016/j.physd.2011.06.020
published as Physica D 240 (2011), no. 19, 1510-1515 · Final version, to appear in Physica D (2011)
openalex publication_date 2011/07/07 · arxiv created 2011/07/18 · arxiv updated 2013/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct classes of two-dimensional aperiodic Lorentz systems that have infinite horizon and are 'chaotic', in the sense that they are (Poincaré) recurrent, uniformly hyperbolic, ergodic, and the first-return map to any scatterer is K-mixing. In the case of the Lorentz tubes (i.e., Lorentz gases in a strip), we define general measured families of systems (ensembles) for which the above properties occur with probability 1. In the case of the Lorentz gases in the plane, we define families, endowed with a natural metric, within which the set of all chaotic dynamical systems is uncountable and dense.