Experimental Mathematics

Solving the sextic by iteration: a study in complex geometry and dynamics

Scott Crass

Abstract

We use the Valentiner action of \A{6} on \funnyC\funnyP$^2$ to develop an iterative algorithm for the solution of the general sextic equation over \funnyC, analogous to Doyle and McMullen's algorithm for the quintic.

Article information

Source
Experiment. Math. Volume 8, Issue 3 (1999), 209-240.

Dates
First available in Project Euclid: 9 March 2003

Permanent link to this document
http://projecteuclid.org/euclid.em/1047262404

Mathematical Reviews number (MathSciNet)
MR1724156

Zentralblatt MATH identifier
01442125

Subjects
Primary: 14N99: None of the above, but in this section
Secondary: 14H45: Special curves and curves of low genus 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04] 37F50: Small divisors, rotation domains and linearization; Fatou and Julia sets

Citation

Crass, Scott. Solving the sextic by iteration: a study in complex geometry and dynamics. Experiment. Math. 8 (1999), no. 3, 209--240. http://projecteuclid.org/euclid.em/1047262404.


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