Scaling Ratios and Triangles in Siegel Disks
| dc.creator | Buff, Xavier | |
| dc.creator | Henriksen, Christian | |
| dc.date | 1999-05-27 | |
| dc.date.accessioned | 2026-07-07T05:29:16Z | |
| dc.date.available | 2026-07-07T05:29:16Z | |
| dc.description | Let $f(z)=e^{2iπθ} z+z^2$, where $θ$ is a quadratic irrational. McMullen proved that the Siegel disk for $f$ is self-similar about the critical point. We give a lower bound for the ratio of self-similarity, and we show that if $θ=(\sqrt 5-1)/2$ is the golden mean, then there exists a triangle contained in the Siegel disk, and with one vertex at the critical point. This answers a 15 year old conjecture. | |
| dc.description | 13 pages, 13 PostScript figures | |
| dc.identifier | https://arxiv.org/abs/math/9905173 | |
| dc.identifier | http://arxiv.org/abs/math/9905173 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78569 | |
| dc.subject | Dynamical Systems | |
| dc.title | Scaling Ratios and Triangles in Siegel Disks | |
| dc.type | text |