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Weakly expanding skew-products of quadratic maps

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. Alves for skew-products over the linear strongly expanding map of the circle.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693138
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Submitted on : Tuesday, May 1, 2012 - 9:44:35 PM
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Jerome Buzzi, Olivier Sester, Masato Tsujii. Weakly expanding skew-products of quadratic maps. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2003, 23 (5), pp.1401-1414. ⟨10.1017/S0143385702001694⟩. ⟨hal-00693138⟩

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