A family of critically finite maps with symmetry
| dc.creator | Crass, Scott | |
| dc.date | 2003-07-03 | |
| dc.date | 2005-05-17 | |
| dc.date.accessioned | 2026-07-07T04:59:25Z | |
| dc.date.available | 2026-07-07T04:59:25Z | |
| dc.description | The symmetric group S_n acts as a reflection group on CP^{n-2} (for $n\geq 3$) . Associated with each of the $\binom{n}{2}$ transpositions in S_n is an involution on CP^{n-2} that pointwise fixes a hyperplane--the mirrors of the action. For each such action, there is a unique S_n-symmetric holomorphic map of degree n+1 whose critical set is precisely the collection of hyperplanes. Since the map preserves each reflecting hyperplane, the members of this family are critically-finite in a very strong sense. Considerations of symmetry and critical-finiteness produce global dynamical results: each map's fatou set consists of a special finite set of superattracting points whose basins are dense. | |
| dc.description | 24 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/math/0307057 | |
| dc.identifier | http://arxiv.org/abs/math/0307057 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67976 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37F45 | |
| dc.title | A family of critically finite maps with symmetry | |
| dc.type | text |