Rational Maps Whose Fatou Components Are Jordan Domains
| dc.creator | Pilgrim, Kevin M. | |
| dc.date | 1994-12-19 | |
| dc.date.accessioned | 2026-07-07T09:15:14Z | |
| dc.date.available | 2026-07-07T09:15:14Z | |
| dc.description | We prove: If $f(z)$ is a critically finite rational map which has exactly two critical points and which is not conjugate to a polynomial, then the boundary of every Fatou component of $f$ is a Jordan curve. If $f(z)$ is a hyperbolic critically finite rational map all of whose postcritical points are periodic, then there exists a cycle of Fatou components whose boundaries are Jordan curves. We give examples of critically finite hyperbolic rational maps $f$ with the property that on the closure of a Fatou component $Ω$ satisfying $f(Ω)=Ω$, $f|_{\bdry Ω}$ is not topologically conjugate to the dynamics of any polynomial on its Julia set. | |
| dc.description | Separate uu-encoded "tar" file of figures sent also. Uses Latex2.09 and geompsfi.sty | |
| dc.identifier | https://arxiv.org/abs/math/9412205 | |
| dc.identifier | http://arxiv.org/abs/math/9412205 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152948 | |
| dc.subject | Dynamical Systems | |
| dc.title | Rational Maps Whose Fatou Components Are Jordan Domains | |
| dc.type | text |