Analytic skew-products of quadratic polynomials over Misiurewicz-Thurston maps

Rui Gao; Weixiao Shen

doi:10.3934/dcds.2014.34.2013

Article Contents

2014, Volume 34, Issue 5: 2013-2036. Doi: 10.3934/dcds.2014.34.2013

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Analytic skew-products of quadratic polynomials over Misiurewicz-Thurston maps

Rui Gao^1, and
Weixiao Shen^1,

1.
Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, 119076

Received: August 31, 2012

Revised: July 31, 2013

Published: April 2014

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Abstract

We consider skew-products of quadratic maps over certain Misiurewicz-Thurston maps and study their statistical properties. We prove that, when the coupling function is a polynomial of odd degree, such a system admits two positive Lyapunov exponents almost everywhere and a unique absolutely continuous invariant probability measure.

Keywords:

Lyapunov exponent,
absolutely continuous invariant measure,
non-uniform expansion,
Viana maps,
Misiurewicz-Thurston maps.

Mathematics Subject Classification: Primary: 37D25; Secondary: 37C40.

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