Hyperbolic components and cubic polynomials

Abstract

In the space of cubic polynomials, Milnor defined a notable curve ${\mathcal{S}}_p$, consisting of cubic polynomials with a periodic critical point, whose period is exactly $p$. In this paper, we show that for any integer $p\ge 1$, any bounded hyperbolic component on ${\mathcal{S}}_p$ is a Jordan disk.

36 pages, 9 figures

Cited by in corpus (1)

• On geometrically finite degenerations I: boundaries of main hyperbolic components