# 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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