University of Illinois Urbana-Champaign

Julia Sets and Symbolic Dynamics of Certain Rational and Entire Functions

Niamsup, Piyapong

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Description

Title
Julia Sets and Symbolic Dynamics of Certain Rational and Entire Functions
Author(s)
Niamsup, Piyapong
Issue Date
1997
Doctoral Committee Chair(s)
Palmore, Julian
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
A complex analytic map f always decomposes the complex plane into two dis-joint subsets, the Julia set J(f) on which the family of iterates of f, $\{f\sp{k}\}\sbsp{k=0}{\infty}$, fails to be a normal family, and its complement, the Fatou set F(f). The dynamics of f on its Fatou set is relatively tame while the dynamics on its Julia set is always complicated. We study the Julia sets and Symbolic dynamics of certain rational and entire functions. We also estimate the size of some Julia sets in terms of their Hausdorff dimension.
Graduation Semester
1997
Type of Resource
text
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http://hdl.handle.net/2142/86942

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