Abstract
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.
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Acknowledgements
The research of the Mariusz Urbański was supported in part by the NSF Grant DMS 0700831.
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Skorulski, B., Urbański, M. (2013). The Law of Iterated Logarithm and Equilibrium Measures Versus Hausdorff Measures for Dynamically Semi-regular Meromorphic Functions. In: Barral, J., Seuret, S. (eds) Further Developments in Fractals and Related Fields. Trends in Mathematics. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8400-6_11
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