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Derivative formula of the potential function for generalized SRB measures of hyperbolic systems of codimension one

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  • Under the condition that unstable manifolds are one dimensional, the derivative formula of the potential function of the generalized SRB measure with respect to the underlying dynamical system is extended from the hyperbolic attractor case to the general case when the hyperbolic set intersecting with unstable manifolds is a Cantor set. It leads to derivative formulas of objects and quantities that characterize a uniformly hyperbolic system, including the generalized SBR measure and its entropy, the root of the Bowen's equation, and the Hausdorff dimension of the hyperbolic set on a dimension two Riemannian manifold.
    Mathematics Subject Classification: Primary: 37D20, 37D35; Secondary: 37C40, 37C45.

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