Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T09:35:16.505Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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