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Documents  Critères de recherche : "Thermodynamic formalism" | enregistrements trouvés : 6

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Research schools;Dynamical Systems and Ordinary Differential Equations

I will present some joint works with Volker Mayer in which we primarily show that for a large class of entire and meromorphic transcendental functions the full geometric thermodynamic formalism holds. Most notably, this means that the transfer operators generated by geometric potentials are well dened and bounded after an appropriate conformal change of Riemannian metric on the complex plane C. We show that these operators are quasi-compact of diagonal type with one leading eigenvalue, which in addition is simple. In particular, the dual operators have positive eigenvalues and eigenvectors that are Borel probability eigenmeasures. The probability measure obtained by integrating these eigenmeasures against leading eigenfanctions of transfer operators are invariant. We show that these measures are equilibrium states of geometric potentials. The primary applications of these theorems capture the stochastic laws such as exponential decay of correlations, the central limit theorem, and the law of iterated logarithm. it also permits us to provide exact formulas (of Bowen’s type) for Hausdorff dimension of radial Julia sets and multifractal analysis. We will discuss two distinct routes (leading to different though overlapping classes of meromorphic transcendental functions) to get the geometric thermodynamic formalism. One of them is based on Nevanlina’s theory and the other on analogues of integral means spectrum from classical complex analysis of conformal maps. I will present some joint works with Volker Mayer in which we primarily show that for a large class of entire and meromorphic transcendental functions the full geometric thermodynamic formalism holds. Most notably, this means that the transfer operators generated by geometric potentials are well dened and bounded after an appropriate conformal change of Riemannian metric on the complex plane C. We show that these operators are quasi-compact of ...

37D35 ; 30D35

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ISBN 978-0-8218-1948-7

SMF/AMS texts and monographs , 0002

Localisation : Collection 1er étage

système dynamique différentiable # thermodynamique # théorie de mesure # théorie ergodique

28Dxx ; 30-XX ; 80-XX ; 82Bxx

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- 183 p.
ISBN 978-0-201-13504-6

Encyclopedia of mathematics and its applications , 0005

Localisation : Collection 1er étage

formalisme thermodynamique # équilibre classique # mécanique statistique

82-02

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- V-107 p.
ISBN 978-0-8218-4659-9

Memoirs of the american mathematical society , 0954

Localisation : Collection 1er étage

fonction méromorphe # fonction des variables complexes # fractales # fonction transcendentale

30-02 ; 37-02 ; 30Dxx ; 37F10 ; 30D05

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- xii; 297 p.
ISBN 978-3-0348-0205-5

Progress in mathematics , 0294

Localisation : Collection 1er étage

système dynamique # analyse multifractale # formalisme thermodynamique

37D35 ; 37D20 ; 37D25 ; 37C45 ; 37-02 ; 37N20

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- x; 112 p.
ISBN 978-3-642-23649-5

Lecture notes in mathematics , 2036

Localisation : Collection 1er étage

système dynamique aléatoire # mesure de Gibbs # opérateur de Ruelle

37-XX ; 37-02 ; 37MXX

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