A family of critically finite maps with symmetry
Abstract
The symmetric group S_n acts as a reflection group on CP^{n2} (for $n\geq 3$) . Associated with each of the $\binom{n}{2}$ transpositions in S_n is an involution on CP^{n2} that pointwise fixes a hyperplanethe mirrors of the action. For each such action, there is a unique S_nsymmetric 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 criticallyfinite in a very strong sense. Considerations of symmetry and criticalfiniteness produce global dynamical results: each map's fatou set consists of a special finite set of superattracting points whose basins are dense.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2003
 DOI:
 10.48550/arXiv.math/0307057
 arXiv:
 arXiv:math/0307057
 Bibcode:
 2003math......7057C
 Keywords:

 Dynamical Systems;
 37F45
 EPrint:
 24 pages, 9 figures