Cubic Siegel polynomials and the bifurcation measure
Dynamical Systems
2024-10-29 v1 Complex Variables
Abstract
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. This answers a question of Dujardin in positive. Our result implies the existence of holomorphic disks in the support of the bifurcation measure, and also implies that the set of rigid parameters is not closed in the moduli space of cubic polynomials.
Keywords
Cite
@article{arxiv.2410.20179,
title = {Cubic Siegel polynomials and the bifurcation measure},
author = {Matthieu Astorg and Davoud Cheraghi and Arnaud Chéritat},
journal= {arXiv preprint arXiv:2410.20179},
year = {2024}
}