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

Abstract

top
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.

How to cite

top

Bullett, 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
  1. 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
  2. Bullett (S.) and Haïssinsky (P.).— Pinching holomorphic correspondences, Conformal Geometry and Dynamics 11, p. 65-89 (2007). Zbl1138.37022MR2314243
  3. 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
  4. Bullett (S.) and Penrose (C.).— Mating quadratic maps with the modular group, Inventiones Math. 115, p. 483-511 (1994). Zbl0801.30025MR1262941
  5. Curtis (A.).— PhD Thesis, QMUL (2013). 
  6. Milnor (J.).— Dynamics in One Complex Variable, Annals of Mathematics Studies No. 160, Princeton University Press (2006). Zbl1085.30002MR2193309

NotesEmbed ?

top

You must be logged in to post comments.