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The Denjoy type of argument for quasiperiodically forced circle diffeomorphisms

Published online by Cambridge University Press:  17 March 2006

TOBIAS H. JÄGER  and
GERHARD KELLER
TOBIAS H. JÄGER
Affiliation:
Mathematisches Institut, Friedrich-Alexander-Universität, Erlangen-Nürnberg, Germany (e-mail: jaeger@mi.uni-erlangen.de, keller@mi.uni-erlangen.de)
GERHARD KELLER
Affiliation:
Mathematisches Institut, Friedrich-Alexander-Universität, Erlangen-Nürnberg, Germany (e-mail: jaeger@mi.uni-erlangen.de, keller@mi.uni-erlangen.de)
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Abstract

We carry the argument used in the proof of Denjoy's theorem over to the quasiperiodically forced case. Thus we derive that, if a system of quasiperiodically forced circle diffeomorphisms with bounded variation of the derivative has no invariant graphs with a certain kind of topological regularity, then the system is topologically transitive.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 2 , April 2006 , pp. 447 - 465
Copyright
2006 Cambridge University Press

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