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Rational maps represented by both rabbit and aeroplane matings

Exall, Freddie (2011) Rational maps represented by both rabbit and aeroplane matings. Doctoral thesis, University of Liverpool.

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Abstract

Understanding parameter spaces of rational maps is an active area of complex dynamics. There is a region of a particular parameter space of rational maps which contains all possible matings with the rabbit polynomial in a well understood manner. In an effort to further understand which hyperbolic components of the parameter space correspond to matings with the aeroplane we relate the family of matings with the aeroplane to the family of matings with the rabbit. We present an algorithm, described in chapter 3, which calculates the mating with the rabbit which is Thurston equivalent to a given post-critically finite mating with the aeroplane. Chapter 4 gives a result describing which matings with the rabbit are Thurston equivalent to some mating with the aeroplane. Chapter 5 studies the algorithm in more detail, giving results bounding the number of steps required for the algorithm to produce a result.

Item Type:Thesis (Doctoral)
Additional Information:Windows users: In order to open supplementary file, the programme 7-Zip File Manager should be used. After files are extracted, view readme.txt file for instructions on using data. If any difficulties are experienced, please contact the author directly at freddie_signup@gmx.co.uk
Uncontrolled Keywords:complex dynamics; shared mating; aeroplane; rabbit; rational map; julia set lamination; Thurston
Subjects:Q Science > QA Mathematics
Departments, Research Centres and Related Units:Academic Faculties, Institutes and Research Centres > Faculty of Science > Department of Mathematical Sciences
Status:Unpublished
ID Code:3393
Deposited On:30 Nov 2011 15:22
Last Modified:30 Jan 2012 08:46

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