1999/03/09 by Scott Crass, Crass, Scott
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS
paper · pdf · doi:10.48550/arxiv.math/9903054
40 pages, 15 figures
arxiv created 1999/10/06 · arxiv updated 2009/11/30
The requirement for solving a polynomial is a means of breaking its symmetry, which in the case of the quintic, is that of the symmetric group S5. Induced by its five-dimensional linear permutation representation is a three-dimensional projective action. A mapping of complex projective 3-space with this S5 symmetry can provide the requisite symmetry-breaking tool. The article describes some of the S5 geometry in CP3 as well as several maps with particularly elegant geometric and dynamical properties. Using a rational map in degree six, it culminates with an explicit algorithm for solving a general quintic. In contrast to the Doyle-McMullen procedure - three 1-dimensional iterations, the present solution employs one 3-dimensional iteration.