Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 12 of 12 for “"Julia sets."”.
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Completely Invariant Julia Sets of Rational Semigroups
We also develop some of the theory of Iterated Function Systems that seems to have particular importance to the study of rational semigroups.
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Accuracy of Computer Generated Approximations to Julia Sets
A Julia set for a complex function 𝑓 is the set of all points in the complex plane where the iterates of 𝑓 do not form a normal family. A picture of the Julia set for a function can be generated with a computer by coloring pixels (which we consider to be small squares) based on the behavior of the …
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Julia Sets and Symbolic Dynamics of Certain Rational and Entire Functions
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997.
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On the Dynamics of Quasi-Self-Matings of Generalized Starlike Complex Quadratics and the Structure of the Mated Julia Sets
<p>It has been shown that, in many cases, Julia sets of complex polynomials can be "glued" together to obtain a new Julia set homeomorphic to a Julia set of a rational map; the dynamics of the two polynomials are reflected in the dynamics of the mated rational map. Here, I investigate the Julia …
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Dynamics of Cubic Rational Maps Under Certain Constraints on Critical Points
<p>There is a neat dichotomy for the Julia sets of quadratic rational maps; that is, they are either connected or a Cantor set. In contrast to the quadratic case, the Julia sets of rational maps of of degree ≥ 3 have more variations. In this project, we study the Julia sets of cubic rational maps …
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Indecomposability in inverse limits.
… we investigate classical inverse limits of Julia sets and set-valued inverse limits of arbitrary compacta. Using the theory of Hubbard trees, the trunk of the Julia set of a postcriticallly finite polynomial is introduced. Using this trunk, a characterization of indecomposability is provided …
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Hubbard trees and their properties.
… tree is a set of points at the core of dendritic Julia sets. These trees encapsulate all the information about the larger Julia set, but in a much smaller, easier to understand structure. We discuss the structure of Hubbard trees, in particular, we provide a useful definition of branch point and …
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Dynamical statistics for power series and polynomials with restricted coefficients
… consider a family of fractals arising as limit sets of pairs of similitudes; these fractals are closely related to power series with all coefficients equal to ±1. Motivated by the Julia–Mandelbrot correspondence, we construct a natural measure in the parameter space satisfying analogous …
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Estimating the Hausdorff dimension
… tree is planted in the wild. The dimensions of Julia sets and of the Hénon attractor were also investigated. A computer program for calculating the estimates is included.
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Composition Sequences and Semigroups of Möbius Transformations
… Like Kleinian groups, semigroups have limit sets, and indeed each semigroup is equipped with two limit sets. We find that limit sets have an internal structure with features similar to the limit sets of Kleinian groups and the Julia sets of iterates of analytic functions. We introduce the …
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Rates Of Escape Under Iteration Of Analytic Functions
In this thesis we focus on sets with a uniform rate of escape under the iteration of transcendental entire functions. We study their properties and their structure as well as using them as a tool to prove some interesting topological results. First, motivated by the work of Rippon and Stallard, we …