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Circle diffeomorphisms forced by expanding circle maps

Published online by Cambridge University Press:  01 November 2011

ALE JAN HOMBURG
ALE JAN HOMBURG*
Affiliation:
KdV Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands Department of Mathematics, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands (email: [email protected])
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Abstract

We discuss the dynamics of skew product maps defined by circle diffeomorphisms forced by expanding circle maps. We construct an open class of such systems that are robustly topologically mixing and for which almost all points in the same fiber converge under iteration. This property follows from the construction of an invariant attracting graph in the natural extension, a skew product of circle diffeomorphisms forced by a solenoid homeomorphism.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 6 , December 2012 , pp. 2011 - 2024
Copyright
Copyright © Cambridge University Press 2011

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