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April  2007, 1(2): 175-203. doi: 10.3934/jmd.2007.1.175

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

Scott Crass 1,

1. 

Mathematics Department, The California State University at Long Beach, Long Beach, CA 90840-1001, United States

Received  September 2006 Published  January 2007

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 certain "heptic" equations in $H$.
Keywords: reflection group, equivariant map, complex dynamics, seventh-degree equation..
Mathematics Subject Classification: 37C30, 37D3.
Citation: Scott Crass. Solving the heptic by iteration in two dimensions: Geometry and dynamics under Klein's group of order 168. Journal of Modern Dynamics, 2007, 1 (2) : 175-203. doi: 10.3934/jmd.2007.1.175
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