Return time statistics via inducing

2000/10/24 by Henk Bruin, Benoit Saussol, Serge Troubetzkoy +1 · 1 citation
Mathematics · #math.DS #msc:37B20 #msc:37D35 #msc:37F10

paper · pdf

published as Ergodic Theory and Dynamical Systems 23 (2003) 991-1013

arxiv created 2000/10/24 · arxiv updated 2009/11/30

Abstract

We prove that return time statistics of a dynamical system do not change if one passes to an induced (i.e. first return) map. We apply this to show exponential return time statistics in i) smooth interval maps with nowhere-dense critical orbits and ii) certain interval maps with neutral fixed points. The method also applies to iii) certain quadratic maps of the complex plane.

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