Hostname: page-component-7c8c6479df-27gpq Total loading time: 0 Render date: 2024-03-28T20:15:50.178Z Has data issue: false hasContentIssue false

Weakly expanding skew-products of quadratic maps

Published online by Cambridge University Press:  23 September 2003

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)

Abstract

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.

Type
Research Article
Copyright
2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)