No invariant line fields on Cantor Julia sets
In this paper, we prove that a rational map with a Cantor Julia set carries no invariant line field on its Julia set. It follows that a structurally stable rational map with a Cantor Julia set is hyperbolic.
Gespeichert in:
| Veröffentlicht in: | Forum mathematicum 2010-01, Vol.22 (1), p.75-94, Article 75 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | In this paper, we prove that a rational map with a Cantor Julia set carries no invariant line field on its Julia set. It follows that a structurally stable rational map with a Cantor Julia set is hyperbolic. |
|---|---|
| ISSN: | 0933-7741 1435-5337 |
| DOI: | 10.1515/forum.2010.004 |