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

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


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