Solving the heptic in two dimensions: Geometry and dynamics under Klein's group of order 168

Details Solving the heptic in two dimensions: Geometry and dynamics under Klein's group of order 168 Solving the heptic in two dimensions: Geometry and dynamics under Klein's group of order 168

2006-01-16

arxiv.org/abs/math/0601394v1

Mathematics

Dynamical Systems

28 pages, ten figures

Scientific paper

There is a family of seventh-degree polynomials $H$ whose members possess the symmetries of a simple group of order 168. This group has an elegant action on the complex projective plane. Developing some of the action's rich algebraic and geometric properties rewards us with a special map that also realizes the 168-fold symmetry. The map's dynamics provides the main tool in an algorithm that solves "heptic" equations in $H$.

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