A classification of bicritical rational maps with a pair of period two superattracting cycles

Adam Epstein[1]; Thomas Sharland[2]

  • [1] University of Warwick, Coventry, CV4 7AL, UK
  • [2] State University of New York at Stony Brook, Stony Brook, New York, USA

Annales de la faculté des sciences de Toulouse Mathématiques (2012)

  • Volume: 21, Issue: S5, page 907-934
  • ISSN: 0240-2963

Abstract

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We give a Thurston classification of those bicritical rational maps which have two period two superattracting cycles. We also show that all such maps are constructed by the mating of two unicritical degree d polynomials.

How to cite

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Epstein, Adam, and Sharland, Thomas. "A classification of bicritical rational maps with a pair of period two superattracting cycles." Annales de la faculté des sciences de Toulouse Mathématiques 21.S5 (2012): 907-934. <http://eudml.org/doc/251015>.

@article{Epstein2012,
abstract = {We give a Thurston classification of those bicritical rational maps which have two period two superattracting cycles. We also show that all such maps are constructed by the mating of two unicritical degree $d$ polynomials.},
affiliation = {University of Warwick, Coventry, CV4 7AL, UK; State University of New York at Stony Brook, Stony Brook, New York, USA},
author = {Epstein, Adam, Sharland, Thomas},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {12},
number = {S5},
pages = {907-934},
publisher = {Université Paul Sabatier, Toulouse},
title = {A classification of bicritical rational maps with a pair of period two superattracting cycles},
url = {http://eudml.org/doc/251015},
volume = {21},
year = {2012},
}

TY - JOUR
AU - Epstein, Adam
AU - Sharland, Thomas
TI - A classification of bicritical rational maps with a pair of period two superattracting cycles
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2012/12//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - S5
SP - 907
EP - 934
AB - We give a Thurston classification of those bicritical rational maps which have two period two superattracting cycles. We also show that all such maps are constructed by the mating of two unicritical degree $d$ polynomials.
LA - eng
UR - http://eudml.org/doc/251015
ER -

References

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  9. Sharland (T.).— Constructing rational maps with cluster points using the mating operation, J. Lond. Math. Soc., to appear (2012). 
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