Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures

By Luís Barreira. 2006

91 citations recorded by the source corpus.

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.

Subfields: Biomedical Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cd4d4e2066d123f0294a7ee0505c6bace4fbbf7a

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In Biomedical Engineering

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Equidistribution from fractal measures (2013, background): “This is a broader class than Gibbs measures for Hölder potentials; for example, it contains Gibbs measures for almost-additive sequences of potentials, see [1].”
The thermodynamic formalism for sub-additive potentials (2007, methodology): “We point out that Falconer and Barreira had some earlier contributions in the study of thermodynamic formalism for sub-additive potentials.”
Almost additive multifractal analysis (2009, unknown): “Proceeding as in the proof of Theorem 3 in [2] we obtain a sequence (nk,i)k of natural numbers such that −δ + φ i nk,i (x) nk,i lim n→∞ 1 n ∫”