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STATISTICAL PROPERTIES OF GENERALIZED HORSESHOE MAPS ABBAS FAKHARI AND MOHAMMAD SOUFI
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Abstract. We apply thermodynamic formalism to a generalized horseshoe map. We prove that a tailored anisotropic Banach space with weighted norms yields a spectral gap for the transfer operator, implying the existence of a unique physical measure. Under the virtually expanding condition, this measure is absolutely continuous with respect to Lebesgue measure, with density in the Sobolev space Hµ, for some µ< 1/2.
Title: STATISTICAL PROPERTIES OF GENERALIZED HORSESHOE MAPS ABBAS FAKHARI AND MOHAMMAD SOUFI
Description:
Abstract.
We apply thermodynamic formalism to a generalized horseshoe map.
We prove that a tailored anisotropic Banach space with weighted norms yields a spectral gap for the transfer operator, implying the existence of a unique physical measure.
Under the virtually expanding condition, this measure is absolutely continuous with respect to Lebesgue measure, with density in the Sobolev space Hµ, for some µ< 1/2.
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