The Law of Iterated Logarithm and Equilibrium Measures Versus Hausdorff Measures for Dynamically Semi-regular Meromorphic Functions

Part of the Trends in Mathematics book series (TM)


The Law of Iterated Logarithm for dynamically semi-regular meromorphic mappings and loosely tame observables is established. The equilibrium states of tame potentials are compared with an appropriate one-parameter family of generalized Hausdorff measures. The singularity/absolute continuity dichotomy is established. Both results utilize the concept of nice sets and the theory of infinite conformal iterated function systems.


Invariant Measure Meromorphic Function Hausdorff Measure Iterate Logarithm Iterate Function System 
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The research of the Mariusz Urbański was supported in part by the NSF Grant DMS 0700831.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad Católica del NorteAntofagastaChile
  2. 2.Department of MathemsaticsUniversity of North TexasDentonUSA

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