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Weakly expanding skew-products of quadratic maps

Published online by Cambridge University Press:  23 September 2003

JÉRÔME BUZZI,
OLIVIER SESTER and
MASATO TSUJII
JÉRÔME BUZZI
Affiliation:
Centre de Mathématiques de l'Ecole Polytechnique, CNRS UMR 7640, 91128 Palaiseau, France (e-mail: buzzi@math.polytechnique.fr)
OLIVIER SESTER
Affiliation:
Laboratoire d'Analyse et de Mathématiques Appliquées, CNRS UMR 8050, Université de Marne-la-Vallé, 5 boulevard Descartes, Champs sur Marne, 77454 Marne-la-Vallée Cedex 2, France (e-mail: sester@math.univ-mlv.fr)
MASATO TSUJII
Affiliation:
Departement of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo, 060-0810, Japan (e-mail: tsujii@math.sci.hokudai.ac.jp)
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Abstract

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We consider quadratic skew-products over angle-doubling of the circle and prove that they admit positive Lyapunov exponents almost everywhere and an absolutely continuous invariant probability measure. This extends corresponding results of M. Viana and J. F. Alvès for skew-products over the linear strongly expanding map of the circle.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 5 , October 2003, pp. 1401 - 1414
Copyright
2003 Cambridge University Press