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 |
Acceso al artículo completo |