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Spectra of dimensions for Poincaré recurrences

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  • The spectra of Poincaré recurrences for two classes of dynamical systems are obtained in the framework of the Carathéodory construction. One class contains systems which are topologically conjugate to subshifts with the specification property, the other consists of minimal multipermutative symbolic systems. The spectra are shown to be solutions of a non-homogeneous Bowen equation, and their relationship with multifractal spectra of Lyapunov exponents is exposed.
    Mathematics Subject Classification: 37C45.

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