University of Illinois Urbana-Champaign

Cremer Points and Critical Points in Complex Dynamics

Petracovici, Lia

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https://hdl.handle.net/2142/86821

Description

Title
Cremer Points and Critical Points in Complex Dynamics
Author(s)
Petracovici, Lia
Issue Date
2003
Doctoral Committee Chair(s)
Aimo Hinkkanen
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
In 2000, Kiwi proved that polynomials with a Cremer fixed point having the small cycles 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 point that is approximated by small cycles, have a critical point that is not accessible from the complement of the Julia set.
Graduation Semester
2003
Type of Resource
text
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http://hdl.handle.net/2142/86821

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