2025/04/27 by Petersen, Carsten Lunde, Zakeri, Saeed
#37F10 #37F20 #37F25 #37F31 #37F46 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.19081
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 ↦ 2t (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.