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Return time statistics via inducing

Published online by Cambridge University Press:  01 August 2003

H. BRUIN ,
B. SAUSSOL ,
S. TROUBETZKOY  and
S. VAIENTI
H. BRUIN
Affiliation:
Department of Mathematics, University of Groningen, PO Box 800, 9700 AV Groningen, the Netherlands (e-mail: bruin@math.rug.nl)
B. SAUSSOL
Affiliation:
Laboratoire Amiénois de Mathémathiques Fondamentales et Appliquées, Université de Picardie–Jules Verne, 33 rue St Leu, 80039 Amiens Cedex 1, France (e-mail: benoit.saussol@mathinfo.u-picardie.fr)
S. TROUBETZKOY
Affiliation:
Institut de Mathématiques de Luminy, FRUMAM, Fédération de Recherche des Unités de Mathématiques de Marseille, CNRS Luminy, Case 907, F-13288 Marseille Cedex 9, France (e-mail: serge@cpt.univ-mrs.fr, troubetz@iml.univ-mrs.fr) Centre de Physique Théorique, FRUMAM, Fédération de Recherche des Unités de Mathématiques de Marseille, CNRS Luminy, Case 907, F-13288 Marseille Cedex 9, France (e-mail: vaienti@cpt.univ-mrs.fr)
S. VAIENTI
Affiliation:
Centre de Physique Théorique, FRUMAM, Fédération de Recherche des Unités de Mathématiques de Marseille, CNRS Luminy, Case 907, F-13288 Marseille Cedex 9, France (e-mail: vaienti@cpt.univ-mrs.fr)
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Abstract

We prove that the 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 4 , August 2003 , pp. 991 - 1013
Copyright
2003 Cambridge University Press

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