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Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures
The nonadditive thermodynamic formalism is a generalization of the
classical thermodynamic formalism, in which the topological pressure
of a single function $\phi$ is replaced by the topological pressure
of a sequence of functions $\Phi=(\phi_n)_n$. The theory also
includes a variational principle for the topological pressure,
although with restrictive assumptions on $\Phi$. Our main objective
is to provide a new class of sequences, the so-called almost
additive sequences, for which it is possible not only to establish a
variational principle, but also to discuss the existence and
uniqueness of equilibrium and Gibbs measures. In addition, we give
several characterizations of the invariant Gibbs measures, also in
terms of an averaging procedure over the periodic points.