The thermodynamic formalism for almost-additive sequences

We study the nonadditive thermodynamic formalism for theclass of almost-additive sequences of potentials. We define thetopological pressure PZ(Φ) of an almost-additive sequenceΦ, on a set Z. We give conditions which allow us toestablish a variational principle for the topological pressure. Westate conditions for the existence and uniqueness of equilibriummeasures, and for subshifts of finite type the existence anduniqueness of Gibbs measures. Finally, we compare the results foralmost-additive sequences to the thermodynamic formalism for theclassical (additive) case [10] [11] [3],the sequences studied by Barreira [1],Falconer [5], and that of Feng and Lau [7], [6].