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June  2006, 16(2): 279-305. doi: 10.3934/dcds.2006.16.279

Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures

Luis Barreira 1,

1. 

Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa

Received  December 2005 Published  July 2006

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.
Keywords: thermodynamic formalism., Almost additive sequences.
Mathematics Subject Classification: Primary: 37D3.
Citation: Luis Barreira. Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures. Discrete & Continuous Dynamical Systems, 2006, 16 (2) : 279-305. doi: 10.3934/dcds.2006.16.279
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