Cubic Siegel polynomials and the bifurcation measure
Résumé
We prove that cubic polynomial maps with a fixed Siegel disk and a critical orbit eventually landing inside that Siegel disk lie in the support of the bifurcation measure µ bif . This answers a question of Dujardin in positive. Our result implies the existence of holomorphic disks in the support of µ bif , and also implies that the set of quasi-conformally rigid parameters is not closed in the moduli space of cubic polynomials.
Domaines
Mathématiques [math]| Origine | Fichiers produits par l'(les) auteur(s) |
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