Cremer Points and Critical Points in Complex Dynamics

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Petracovici, Lia

Contributors dc:contributor

• Aimo Hinkkanen

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3101948

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86821