A family of critically finite maps with symmetry.

Título inglés A family of critically finite maps with symmetry.
Título español Una familia de aplicaciones críticamente finitas con simetría.
Autor/es Crass, Scott
Organización Math. Dep. California State Univ., Long Beach CA, Estados Unidos
Revista 0214-1493
Publicación 2005, 49(1): 127-157, 9 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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.
Clasificación UNESCO 120211
Palabras clave español Sistemas dinámicos ; Aplicaciones equivariantes ; Representación de grupos ; Grupo simétrico Sn ; Grupos finitos ; Conjuntos de Julia
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