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arXiv · 2504.19081

Lemon limbs of the cubic connectedness locus

Carsten Lunde Petersen·Saeed Zakeri
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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.

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Carsten Lunde Petersen, Saeed Zakeri. 2025-09-16. Lemon limbs of the cubic connectedness locus. https://arxiv.org/abs/2504.19081

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