Geodesic
The calculus of thermodynamical formalism
Journal of the European Mathematical Society, Tome 20 (2018) no. 10, pp. 2357-2412

Voir la notice de l'article provenant de la source EMS Press

Given an onto map T acting on a metric space Ω and an appropriate Banach space of functions X(Ω), one classically constructs for each potential A∈X a transfer operator LA​ acting on X(Ω). Under suitable hypotheses, it is well-known that LA​ has a maximal eigenvalue λA​, has a spectral gap and defines a unique Gibbs measure μA​. Moreover there is a unique normalized potential of the form B=A+f−f∘T+c acting as a representative of the class of all potentials defining the same Gibbs measure.
DOI : 10.4171/jems/814
Classification : 37-XX, 49-XX
Keywords: Transfer operators, equilibrium states, entropy, regularity, Wasserstein space 
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Paolo Giulietti; Benoît R. Kloeckner; Artur O. Lopes; Diego Marcon. The calculus of thermodynamical formalism. Journal of the European Mathematical Society, Tome 20 (2018) no. 10, pp. 2357-2412. doi: 10.4171/jems/814

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