Rational maps with clustering and the mating of polynomials
Sharland, Thomas Joseph (2010) Rational maps with clustering and the mating of polynomials. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2493178~S15
The main focus of this thesis is the study of a special class of bicritical rational maps of the Riemann sphere. This special property will be called clustering; which informally is when a subcollection of the immediate basins of the two (super-)attracting periodic orbits meet at a periodic point p, and so the basins of the attracting periodic orbits are clustered around the points on the orbit of p. Restricting ourselves to the cases where p is fixed or of period 2, we investigate the structure of such maps combinatorially; in particular showing a very simple collection of combinatorial data is enough to define a rational map uniquely in the sense of Thurston. We also use the language of symbolic dynamics to investigate pairs (f, g) of polynomials such that f - g has a fixed or period two cluster point. We find that that the internal addresses of such maps follow very definite patterns which can be shown to hold in general.
|Item Type:||Thesis or Dissertation (PhD)|
|Subjects:||Q Science > QA Mathematics|
|Library of Congress Subject Headings (LCSH):||Mappings (Mathematics)|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Sponsors:||Engineering and Physical Sciences Research Council (EPSRC)|
|Extent:||xiv, 264 leaves : ill.|
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