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Multiple equivalent matings with the aeroplane polynomial

Published online by Cambridge University Press:  29 July 2009

MARY REES*
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Mathematical Sciences Building, Liverpool L69 7ZL, UK (email: [email protected])

Abstract

We produce arbitrarily large equivalence classes of matings with the aeroplane polynomial. These are obtained via a slight generalization of the technique of proof of a similar result for Wittner captures.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2009

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References

[1]Douady, A. and Hubbard, J. H.. Etudes dynamiques des polynômes complexes (avec la collaboration de P. Lavaurs, Tan Lei et P. Sentenac), Parts I and II (Publications Mathématiques d’Orsay, 84–85). Département de Mathématiques, Université de Paris-Sud, Orsay, 1985.Google Scholar
[2]Douady, A. and Hubbard, J. H.. On the dynamics of polynomial-like mappings. Ann. Sci. École. Norm. Sup. (4) 18 (1985), 287343.CrossRefGoogle Scholar
[3]Luo, J.. Combinatorics and holomorphic dynamics: captures, matings and Newton’s method. PhD Thesis, Cornell University, 1995.Google Scholar
[4]Rees, M.. A partial description of the parameter space of rational maps of degree two: part I. Acta Math. 168 (1992), 1187.CrossRefGoogle Scholar
[5]Rees, M.. A partial description of the parameter space of rational maps of degree two, part 2. Proc. London Math. Soc. 70 (1995), 644690.CrossRefGoogle Scholar
[6]Rees, M.. Views of parameter space, topographer and resident. Astérisque 288 (2003).Google Scholar
[7]Rees, M.. A Fundamental domain for V 3. Preprint, axXiv.org/pdf/0904.0328, submitted.Google Scholar
[8]Rees, M.. The capture map for V 3. In preparation.Google Scholar
[9]Tan, L.. Matings of quadratic polynomials. Ergod. Th. & Dynam. Sys. 12 (1992), 589620.Google Scholar
[10]Wittner, B.. On the bifurcation loci of rational maps of degree two. PhD Thesis, Cornell University, 1988.Google Scholar