Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type

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In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal measure. Then we prove a Bowen's type formula, i.e. we show that the Hausdorff … continued below

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Coiculescu, Ion May 2005.

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This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided by the UNT Libraries to the UNT Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 275 times, with 4 in the last month. More information about this dissertation can be viewed below.

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  • Coiculescu, Ion

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In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal measure. Then we prove a Bowen's type formula, i.e. we show that the Hausdorff dimension of the set of returning points, is the unique zero of the pressure function. We shall also study conjugacies in the family H, perturbation of functions in the family and related dynamical properties. We define Perron-Frobenius operators for some functions naturally associated with functions in the family H and then, using fundamental properties of these operators, we shall prove the important result that the Hausdorff dimension of the subset of returning points depends analytically on the parameter taken from a small open subset of the n-dimensional parameter space.

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  • May 2005

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  • Feb. 15, 2008, 4:08 p.m.

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  • April 13, 2020, 1:35 p.m.

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Coiculescu, Ion. Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type, dissertation, May 2005; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc4783/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .

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