Ergodic Theory and Dynamical Systems

Weakly expanding skew-products of quadratic maps

a1 Centre de Mathématiques de l'Ecole Polytechnique, CNRS UMR 7640, 91128 Palaiseau, France (e-mail:
a2 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:
a3 Departement of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo, 060-0810, Japan (e-mail:

Article author query
buzzi j   [Google Scholar] 
sester o   [Google Scholar] 
tsujii m   [Google Scholar] 


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.

(Received January 3 2002)
(Revised August 29 2002)