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Showing 1 to 10 of 10 for “"Julia set"”.
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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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Investigating the infinite spider's web in complex dynamics
… and geometric properties of certain invariant sets in the dynamics of entire functions, inspired by recent work of Rippon and Stallard. First, we explore the intricate structure of the spider's web fast escaping sets associated with certain transcendental entire functions. Our results are …
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Cremer Points and Critical Points in Complex Dynamics
… property have a non-accessible point in their Julia set. We extend Kiwi's result to the context of rational maps with a completely invariant attracting component. More precisely, we prove that rational functions with a completely invariant (super)attracting Fatou component having a Cremer fixed …
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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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Invariant measures for inner functions
… omitted.] is ergodic if and only if the Julia set is the real line.
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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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Hubbard trees and their properties.
A Hubbard 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 …
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Homeomorphisms on edges of the Mandelbrot set
… form a one-parameter family, and the Mandelbrot set is defined as a subset of the parameter plane: it contains those parameters, such that the Julia set of the corresponding polynomial is connected. Homeomorphisms of subsets of the Mandelbrot set are constructed by quasi-conformal surgery in the …
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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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Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type
… 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 …