A family of critically finite maps with symmetry.
Publicacions Matemàtiques (2005)
- Volume: 49, Issue: 1, page 127-157
- ISSN: 0214-1493
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topCrass, Scott. "A family of critically finite maps with symmetry.." Publicacions Matemàtiques 49.1 (2005): 127-157. <http://eudml.org/doc/41555>.
@article{Crass2005,
abstract = {The symmetric group Sn acts as a reflection group on CPn-2 (for n>=3).Associated with each of the (n2) transpositions in Sn is an involution on CPn-2 that pointwise fixes a hyperplane -the mirrors of the action. For each such action, there is a unique Sn-symmetric holomorphic map of degree n+1 whose critical set is precisely the collection of hyperplanes. Since the map preserves each reflecting hyperplane, the members of this family are critically-finite in a very strong sense. Considerations of symmetry and critical-finiteness produce global dynamical results: each map's Fatou set consists of a special finite set of superattracting points whose basins are dense.},
author = {Crass, Scott},
journal = {Publicacions Matemàtiques},
keywords = {Sistemas dinámicos; Aplicaciones equivariantes; Representación de grupos; Grupo simétrico Sn; Grupos finitos; Conjuntos de Julia; complex dynamics; equivariant map; Fatou set},
language = {eng},
number = {1},
pages = {127-157},
title = {A family of critically finite maps with symmetry.},
url = {http://eudml.org/doc/41555},
volume = {49},
year = {2005},
}
TY - JOUR
AU - Crass, Scott
TI - A family of critically finite maps with symmetry.
JO - Publicacions Matemàtiques
PY - 2005
VL - 49
IS - 1
SP - 127
EP - 157
AB - The symmetric group Sn acts as a reflection group on CPn-2 (for n>=3).Associated with each of the (n2) transpositions in Sn is an involution on CPn-2 that pointwise fixes a hyperplane -the mirrors of the action. For each such action, there is a unique Sn-symmetric holomorphic map of degree n+1 whose critical set is precisely the collection of hyperplanes. Since the map preserves each reflecting hyperplane, the members of this family are critically-finite in a very strong sense. Considerations of symmetry and critical-finiteness produce global dynamical results: each map's Fatou set consists of a special finite set of superattracting points whose basins are dense.
LA - eng
KW - Sistemas dinámicos; Aplicaciones equivariantes; Representación de grupos; Grupo simétrico Sn; Grupos finitos; Conjuntos de Julia; complex dynamics; equivariant map; Fatou set
UR - http://eudml.org/doc/41555
ER -
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