Dynamics Seminar

Sabyasachi Mukherjee

(Stony Brook University)

"Discontinuity of the straightening map in antiholomorphic dynamics"

Date: Wed, June 14, 2017
Time: 11:15
Place: Research I Seminar Room

Abstract: Abstract< In this talk, we will consider the tricorn, the connectedness locus of quadratic antiholomorphic polynomials \({\overline z}^{2}+c\). Our main goal is to demonstrate that every odd period hyperbolic component of the tricorn is the basis of a ‘baby tricorn’ (much like the Mandelbrot set), but the straightening map from any ‘baby tricorn’ to the original one is discontinuous. This is achieved by proving that all non-real ‘umbilical cords’ of the tricorn wiggle, which generalizes a theorem of Hubbard and Schleicher, and settles a conjecture of Hubbard, Milnor and Schleicher.