Siegel Disks and Periodic Rays of Entire Functions
| dc.creator | Rempe, Lasse | |
| dc.date | 2004-08-03 | |
| dc.date | 2008-05-20 | |
| dc.date.accessioned | 2026-07-07T12:32:14Z | |
| dc.date.available | 2026-07-07T12:32:14Z | |
| dc.description | Let f be an entire function whose set of singular values is bounded and suppose that f has a Siegel disk such that f restricts to a homeomorphism of the boundary. We show that the Siegel disk is bounded. Using a result of Herman, we deduce that if additionally the rotation number of the Siegel disk is Diophantine, then its boundary contains a critical point of f. Suppose furthermore that all singular values of f lie in the Julia set. We prove that, if f has a Siegel disk $U$ whose boundary contains no singular values, then the condition that f is a homeomorphism of the boundary of U is automatically satisfied. We also investigate landing properties of periodic dynamic rays by similar methods. | |
| dc.description | 22 pages, 4 figures. A problem with the image quality of some of the figures was fixed. Some minor corrections were also made. Final version | |
| dc.identifier | https://arxiv.org/abs/math/0408041 | |
| dc.identifier | http://arxiv.org/abs/math/0408041 | |
| dc.identifier | J. Reine Angew. Math. 624, 81-102 (2008). | |
| dc.identifier | doi:10.1515/CRELLE.2008.081 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216712 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37F10, 30D05 | |
| dc.title | Siegel Disks and Periodic Rays of Entire Functions | |
| dc.type | text |