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Intermittency in families of unimodal maps

Published online by Cambridge University Press:  09 January 2002

ALE JAN HOMBURG  and
TODD YOUNG
ALE JAN HOMBURG
Affiliation:
Department of Mathematics, Utrecht University, Budapestlaan 6, 3584 CD Utrecht, The Netherlands (e-mail: [email protected]) KdV-Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
TODD YOUNG
Affiliation:
Department of Mathematics, Morton Hall, Ohio University, Athens, OH 45701, USA (e-mail: [email protected])
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Abstract

We consider intermittency in one-parameter families of unimodal maps, induced by saddle node and boundary crisis bifurcations. In these bifurcations either a periodic orbit or a periodic interval disappears to give rise to chaotic bursts. We prove asymptotic formulae for the frequency with which orbits visit the region previously occupied by the attractor. For this, we extend Pianigiani's results on conditionally invariant measures for the logistic family to more general families.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 1 , February 2002 , pp. 203 - 225
Copyright
2002 Cambridge University Press

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