The thermodynamic formalism for almost-additive sequences

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June 2006, 16(2): 435-454. doi: 10.3934/dcds.2006.16.435

The thermodynamic formalism for almost-additive sequences

1.	Penn State University, McAllister Building, State College, PA 16802, United States

Received July 2005 Revised December 2005 Published July 2006

Abstract
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We study the nonadditive thermodynamic formalism for the class of almost-additive sequences of potentials. We define the topological pressure $P_Z(\Phi)$ of an almost-additive sequence $\Phi$, on a set $Z$. We give conditions which allow us to establish a variational principle for the topological pressure. We state conditions for the existence and uniqueness of equilibrium measures, and for subshifts of finite type the existence and uniqueness of Gibbs measures. Finally, we compare the results for almost-additive sequences to the thermodynamic formalism for the classical (additive) case [10] [11] [3], the sequences studied by Barreira [1], Falconer [5], and that of Feng and Lau [7], [6].

Keywords: Thermodynamic formalism, Equilibrium mea-sures, Gibbs measures., Nonadditive sequences.

Mathematics Subject Classification: Primary: 37C40; Secondary: 82B2.

Citation: Anna Mummert. The thermodynamic formalism for almost-additive sequences. Discrete & Continuous Dynamical Systems - A, 2006, 16 (2) : 435-454. doi: 10.3934/dcds.2006.16.435

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