Dynamics Seminar

Event Information Infinitely primitively renormalizable polynomials of bounded type
15:10 on Monday November 16, 2015
16:00 on Monday November 16, 2015
BA6183, Bahen Center, 40 St. George St.
Joe Adams

Stony Brook University

If a complex polynomial acting on the plane admits infinitely many primitive renormalizations of bounded type around each of its critical points, then it's renormalizations all lie in a compact space, the Julia set is locally connected, and the polynomial is combinatorially rigid. In the quadratic case, this amounts to local connectivity of the Mandelbrot set at the corresponding parameter, and it was proven by Jeremy Kahn in 2006. I will define all of these words and illustrate the difficulties that arise from having more than one critical point.