Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures

Abstract

The nonadditive thermodynamic formalism is a generalization of theclassical thermodynamic formalism, in which the topological pressureof a single function $\phi$ is replaced by the topological pressureof a sequence of functions $\Phi=(\phi_n)_n$. The theory alsoincludes a variational principle for the topological pressure,although with restrictive assumptions on $\Phi$. Our main objectiveis to provide a new class of sequences, the so-called almostadditive sequences, for which it is possible not only to establish avariational principle, but also to discuss the existence anduniqueness of equilibrium and Gibbs measures. In addition, we giveseveral characterizations of the invariant Gibbs measures, also interms of an averaging procedure over the periodic points.