2007/03/08 by Nándor Simányi, Nandor Simanyi, Simanyi, Nandor
Mathematics · Physics and Astronomy · #34D05 #37D50 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:34D05 #msc:37D50
paper · pdf · doi:10.48550/arxiv.math/0703215
12 pages
arxiv created 2007/03/08 · openalex publication_date 2007/03/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove the following result, useful and often needed in the study of the ergodic properties of hard ball systems: In any such system, for any phase point x with a non-singular forward trajectory and infinitely many connected collision graphs on that forward orbit, it is true that for any small number epsilon there is a stable tangent vector w of x and a large enough time t>>1 so that the vector w undergoes a contraction by a factor of less than epsilon in time t. Of course, the Multiplicative Ergodic Theorem of Oseledets provides a much stronger conclusion, but at the expense of an unspecified zero-measured exceptional set of phase points, and this is not sufficient in the sophisticated studies the ergodic properties of such flows. Here the exceptional set of phase points is a dynamically characterized set, so that it suffices for the proofs showing how global ergodicity follows from the localone.