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December  2006, 16(4): 857-869. doi: 10.3934/dcds.2006.16.857

Multifractal analysis for the exponential family

Godofredo Iommi 1, and  Bartłomiej Skorulski 2,

1. 

Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
2. 

Institute of Mathematics, Polish Academy of Sciences, Warszawa, Poland

Received  November 2005 Revised  April 2006 Published  September 2006

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.
Keywords: conformal measures., exponential family, Multifractal analysis.
Mathematics Subject Classification: Primary: 37F10, 37D35; Secondary: 30D05, 37F3.
Citation: Godofredo Iommi, Bartłomiej Skorulski. Multifractal analysis for the exponential family. Discrete & Continuous Dynamical Systems, 2006, 16 (4) : 857-869. doi: 10.3934/dcds.2006.16.857
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