Solving the quintic by iteration in three dimensions.
Solving the sextic by iteration: a study in complex geometry and dynamics.
A family of critically finite maps with symmetry.
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...
Polynomials, Symmetry, and Dynamics: an Undertaking in Aesthetics
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