Recurrence rate in rapidly mixing dynamical systems

2004/12/10 by Benoit Saussol, Saussol, Benoit · 2 citations
Mathematics · #37A25 #37B20 #37C45 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37A25 #msc:37B20 #msc:37C45

paper · pdf · doi:10.48550/arxiv.math/0412211

arxiv created 2004/12/10 · arxiv updated 2009/12/01

Abstract

For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of correlation is super-polynomial the recurrence rates and the pointwise dimensions are equal. This gives a broad class of systems for which the recurrence rate equals the Hausdorff dimension of the invariant measure.

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• Shortest distance between observed orbits in distinct Dynamical Systems
• The recurrence spectrum for dynamical systems beyond specification

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