Friday April 4th, 2025 | |
| Time: | 2:15 PM - 3:15 PM |
| Title: | Lemon limbs of the cubic connectedness locus |
| Speaker: | Saeed Zakeri, CUNY |
| Abstract: | |
| We describe a primary limb structure in the connectedness locus of complex cubic polynomials. These limbs are indexed by the periodic points of the angle-doubling map of the circle and are partially visible in the one-dimensional slice of cubics with a fixed critical point, informally known as the ${\rm {\it lemon~ family}}$. The main renormalization locus in each limb is parametrized by the product of a pair of (deleted) 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. The construction includes the intertwining surgery as a special case. Join work with Carsten Petersen. | |