Weakly expanding skew-products of quadratic maps

Jérôme Buzzi; Olivier Sester; Masato Tsujii

doi:10.1017/S0143385702001694

Weakly expanding skew-products of quadratic maps

Jérôme Buzzi, Olivier Sester, Masato Tsujii

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1401-1414
Number of pages	14
Journal	Ergodic Theory and Dynamical Systems
Volume	23
Issue number	5
DOIs	https://doi.org/10.1017/S0143385702001694
Publication status	Published - Oct 2003
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1017/S0143385702001694

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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. Alv{\`e}s for skew-products over the linear strongly expanding map of the circle.",

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AU - Sester, Olivier

AU - Tsujii, Masato

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N2 - 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.

AB - 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.

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JO - Ergodic Theory and Dynamical Systems

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Weakly expanding skew-products of quadratic maps

Abstract

All Science Journal Classification (ASJC) codes

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