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A family of critically finite maps with symmetry
Crass, Scott

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 ; article ; publishedVersion
Matèria: Complex dynamics ; Equivariant map ; Reflection group
Publicat a: Publicacions matematiques, V. 49 N. 1 (2005) , p. 127-157, ISSN 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_49105_06
DOI: 10.5565/128395

31 p, 396.2 KB

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