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

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.

Grantor dc:publisher

University of North Texas

Year dc:date

2005

Author dc:creator

• Coiculescu, Ion

Contributors dc:contributor

• Urbański, Mariusz
• Cherry, William, 1966-
• Clark, Alex

• Dynamics.
• Thermodynamics.
• Perturbation (Mathematics)
• Fractals.
• Geometric function theory.
• Analytic functions.
• family H
• math
• class S
• dynamics
• Hausdorff dimension

Statement dc:rights

• Public
• Copyright
• Coiculescu, Ion
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 61856397
https://digital.library.unt.edu/ark:/67531/metadc4783/
ark: ark:/67531/metadc4783

OAI identifier oai:identifier

info:ark/67531/metadc4783