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

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