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Multifractal analysis for the exponential family

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  • We study the multifractal spectrum for hyperbolic maps from the exponential family. We define a class of potentials for which we prove the existence of conformal measures. Next, we show that the multifractal spectrum of this conformal measure is the Legendre transform of the temperature function. We prove that the domain of the spectrum is unbounded and show that there are two possibilities for its shape.
    Mathematics Subject Classification: Primary: 37F10, 37D35; Secondary: 30D05, 37F35.

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