03353nam 2200613 450 991081162890332120180731044358.01-4704-0568-7(CKB)3360000000465138(EBL)3114086(SSID)ssj0000889263(PQKBManifestationID)11482814(PQKBTitleCode)TC0000889263(PQKBWorkID)10876592(PQKB)11712167(MiAaPQ)EBC3114086(RPAM)15950955(PPN)195418433(EXLCZ)99336000000046513820150417h20092009 uy 0engur|n|---|||||txtccrThermodynamical formalism and multifractal analysis for meromorphic functions of finite order /Volker Mayer, Mariusz UrbańskiProvidence, Rhode Island :American Mathematical Society,2009.©20091 online resource (107 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 203, Number 954"Volume 203, Number 954 (third of 5 numbers)."0-8218-4659-0 Includes bibliographical references and index.""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""""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""Memoirs of the American Mathematical Society ;Volume 203, Number 954.Functions, MeromorphicFunctions of complex variablesFractalsFunctions, Meromorphic.Functions of complex variables.Fractals.515.982SI 130rvkMayer Volker1964-478963Urbański MariuszMiAaPQMiAaPQMiAaPQBOOK9910811628903321Thermodynamical formalism and multifractal analysis for meromorphic functions of finite order3931956UNINA