Solving the quintic by iteration in three dimensions
| dc.creator | Crass, Scott | |
| dc.date | 1999-03-09 | |
| dc.date | 1999-10-06 | |
| dc.date.accessioned | 2026-07-07T05:28:16Z | |
| dc.date.available | 2026-07-07T05:28:16Z | |
| dc.description | 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 S_5. Induced by its five-dimensional linear permutation representation is a three-dimensional projective action. A mapping of complex projective 3-space with this S_5 symmetry can provide the requisite symmetry-breaking tool. The article describes some of the S_5 geometry in CP^3 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. | |
| dc.description | 40 pages, 15 figures | |
| dc.identifier | https://arxiv.org/abs/math/9903054 | |
| dc.identifier | http://arxiv.org/abs/math/9903054 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78197 | |
| dc.subject | Dynamical Systems | |
| dc.title | Solving the quintic by iteration in three dimensions | |
| dc.type | text |