A holomorphic correspondence at the boundary of the Klein combination locus
Shaun Bullett[1]; Andrew Curtis[1]
- [1] School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK
Annales de la faculté des sciences de Toulouse Mathématiques (2012)
- Volume: 21, Issue: S5, page 1119-1137
- ISSN: 0240-2963
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topBullett, Shaun, and Curtis, Andrew. "A holomorphic correspondence at the boundary of the Klein combination locus." Annales de la faculté des sciences de Toulouse Mathématiques 21.S5 (2012): 1119-1137. <http://eudml.org/doc/251006>.
@article{Bullett2012,
abstract = {We investigate an explicit holomorphic correspondence on the Riemann sphere with striking dynamical behaviour: the limit set is a fractal resembling the one-skeleton of a tetrahedron and on each component of the complement of this set the correspondence behaves like a Fuchsian group.},
affiliation = {School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK; School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK},
author = {Bullett, Shaun, Curtis, Andrew},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Kleinian groups; Fuchsian groups; holomorphic correspondences; matings},
language = {eng},
month = {12},
number = {S5},
pages = {1119-1137},
publisher = {Université Paul Sabatier, Toulouse},
title = {A holomorphic correspondence at the boundary of the Klein combination locus},
url = {http://eudml.org/doc/251006},
volume = {21},
year = {2012},
}
TY - JOUR
AU - Bullett, Shaun
AU - Curtis, Andrew
TI - A holomorphic correspondence at the boundary of the Klein combination locus
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2012/12//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - S5
SP - 1119
EP - 1137
AB - We investigate an explicit holomorphic correspondence on the Riemann sphere with striking dynamical behaviour: the limit set is a fractal resembling the one-skeleton of a tetrahedron and on each component of the complement of this set the correspondence behaves like a Fuchsian group.
LA - eng
KW - Kleinian groups; Fuchsian groups; holomorphic correspondences; matings
UR - http://eudml.org/doc/251006
ER -
References
top- Bullett (S.).— A combination theorem for covering correspondences and an application to mating polynomial maps with Kleinian groups, Conformal Geometry and Dynamics 4 (2000) 75-96. Zbl1027.37025MR1755900
- Bullett (S.) and Haïssinsky (P.).— Pinching holomorphic correspondences, Conformal Geometry and Dynamics 11, p. 65-89 (2007). Zbl1138.37022MR2314243
- Bullett (S.) and Harvey (W.).— Mating quadratic maps with Kleinian groups via quasiconformal surgery, Electronic Research Announcements of the AMS 6, p. 21-30 (2000). Zbl1027.37024MR1751536
- Bullett (S.) and Penrose (C.).— Mating quadratic maps with the modular group, Inventiones Math. 115, p. 483-511 (1994). Zbl0801.30025MR1262941
- Curtis (A.).— PhD Thesis, QMUL (2013).
- Milnor (J.).— Dynamics in One Complex Variable, Annals of Mathematics Studies No. 160, Princeton University Press (2006). Zbl1085.30002MR2193309
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