| Data: |
2005 |
| Resum: |
The symmetric group Sn acts as a reflection group on CPn-2 (for n [greater than or equal] 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. |
| Drets: |
Tots els drets reservats.  |
| Llengua: |
Anglès |
| Document: |
Article ; recerca ; Versió publicada |
| Matèria: |
Complex dynamics ;
Equivariant map ;
Reflection group |
| Publicat a: |
Publicacions matemàtiques, V. 49 N. 1 (2005) , p. 127-157, ISSN 2014-4350 |
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