Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of Finite Order.
Mayer, Volker.
Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of Finite Order. - 1st ed. - 1 online resource (120 pages) - Memoirs of the American Mathematical Society ; v.203 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Abstract -- Chapter 1. Introduction -- Chapter 2. Balanced functions -- 2.1. Growth conditions -- 2.2. The precise form of 2 -- 2.3. Classical families -- 2.4. Functions with polynomial Schwarzian derivative -- 2.5. Functions with rational Schwarzian derivative -- 2.6. Uniform balanced growth -- Chapter 3. Transfer operator and Nevanlinna Theory -- 3.1. Choice of a Riemannian metric and transfer operator -- 3.2. Nevanlinna Theory and Borel Sums -- Chapter 4. Preliminaries, Hyperbolicity and Distortion Properties -- 4.1. Dynamical preliminaries and hyperbolicity -- 4.2. Distortion properties -- 4.3. Hölder functions and dynamical Hölder property -- Chapter 5. Perron--Frobenius Operators and Generalized Conformal Measures -- 5.1. Tame potentials -- 5.2. Growth condition and cohomological Perron--Frobenius operator -- 5.3. Topological pressure and existence of conformal measures -- 5.4. Thermodynamical formalism -- 5.5. The support and uniqueness of the conformal measure -- Chapter 6. Finer properties of Gibbs States -- 6.1. The two norm inequality and the spectral gap -- 6.2. Ergodic properties of Gibbs states -- 6.3. Decay of correlations and Central Limit Theorem -- 6.4. Cohomologies and 2=0 -- 6.5. Variational principle -- Chapter 7. Regularity of Perron-Frobenius Operators and Topological Pressure -- 7.1. Analyticity of Perron-Frobenius operators -- 7.2. Analyticity of pressure -- 7.3. Derivatives of the pressure function -- Chapter 8. Multifractal analysis -- 8.1. Hausdorff dimension of Gibbs states -- 8.2. The temperature function -- 8.3. Multifractal analysis -- Chapter 9. Multifractal Analysis of Analytic Families of Dynamically Regular Functions -- 9.1. Extensions of harmonic functions -- 9.2. Holomorphic families and quasi-conformal conjugacies -- 9.3. Real analyticity of the multifractal function -- Bibliography. Index.
9781470405687
Functions, Meromorphic.
Functions of complex variables.
Fractals.
Electronic books.
QA331 -- .M39 2009eb
515.982
Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of Finite Order. - 1st ed. - 1 online resource (120 pages) - Memoirs of the American Mathematical Society ; v.203 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Abstract -- Chapter 1. Introduction -- Chapter 2. Balanced functions -- 2.1. Growth conditions -- 2.2. The precise form of 2 -- 2.3. Classical families -- 2.4. Functions with polynomial Schwarzian derivative -- 2.5. Functions with rational Schwarzian derivative -- 2.6. Uniform balanced growth -- Chapter 3. Transfer operator and Nevanlinna Theory -- 3.1. Choice of a Riemannian metric and transfer operator -- 3.2. Nevanlinna Theory and Borel Sums -- Chapter 4. Preliminaries, Hyperbolicity and Distortion Properties -- 4.1. Dynamical preliminaries and hyperbolicity -- 4.2. Distortion properties -- 4.3. Hölder functions and dynamical Hölder property -- Chapter 5. Perron--Frobenius Operators and Generalized Conformal Measures -- 5.1. Tame potentials -- 5.2. Growth condition and cohomological Perron--Frobenius operator -- 5.3. Topological pressure and existence of conformal measures -- 5.4. Thermodynamical formalism -- 5.5. The support and uniqueness of the conformal measure -- Chapter 6. Finer properties of Gibbs States -- 6.1. The two norm inequality and the spectral gap -- 6.2. Ergodic properties of Gibbs states -- 6.3. Decay of correlations and Central Limit Theorem -- 6.4. Cohomologies and 2=0 -- 6.5. Variational principle -- Chapter 7. Regularity of Perron-Frobenius Operators and Topological Pressure -- 7.1. Analyticity of Perron-Frobenius operators -- 7.2. Analyticity of pressure -- 7.3. Derivatives of the pressure function -- Chapter 8. Multifractal analysis -- 8.1. Hausdorff dimension of Gibbs states -- 8.2. The temperature function -- 8.3. Multifractal analysis -- Chapter 9. Multifractal Analysis of Analytic Families of Dynamically Regular Functions -- 9.1. Extensions of harmonic functions -- 9.2. Holomorphic families and quasi-conformal conjugacies -- 9.3. Real analyticity of the multifractal function -- Bibliography. Index.
9781470405687
Functions, Meromorphic.
Functions of complex variables.
Fractals.
Electronic books.
QA331 -- .M39 2009eb
515.982