Lemon limbs of the cubic connectedness locus
Carsten Lunde Petersen, Saeed Zakeri
公開日: 2025/4/27
Abstract
We describe a primary limb structure in the connectedness locus of complex cubic polynomials, where the limbs are indexed by the periodic points of the doubling map $t \mapsto 2t \ (\operatorname{mod} {\mathbb Z})$. The main renormalization locus in each limb is parametrized by the product of a pair of (punctured) Mandelbrot sets. This parametrization is the inverse of the straightening map and can be thought of as a tuning operation that manufactures a unique cubic of a given combinatorics from a pair of quadratic hybrid classes.