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

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  • 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 $H$.
    Mathematics Subject Classification: 37C30, 37D30.

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