Lemon limbs of the cubic connectedness locus
speaker: Saeed Zakeri (CUNY)abstract: In a joint work with C. L. Petersen, we study special limbs that grow out of the main hyperbolic component of the cubic connectedness locus. These limbs are indexed by the periodic points of the doubling map t 7→ 2t (mod Z) and are partially visible in the one-dimensional slice Per1(0) = {z 7→ z3 + az2}a∈C colloquially known as the lemon family. We exhibit a homeomorphic copy of the product of two Mandelbrot sets in each limb by describing a tuning map that manufactures a unique cubic polynomial from a set of combinatorialanalytic quadratic data (roughly, a periodic point of the doubling map together with a pair of quadratic hybrid classes). The construction includes intertwining surgery as a special case and sheds new light on the straightening of cubic polynomials of disjoint type.
timetable:
Thu 30 May, 10:30 - 11:20, Aula Dini
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