Transcendental dynamics associated with the Feigenbaum fixed point

Dzmitry Dudko

We will consider the unstable manifold of the period-doubling renormalization operator responsible for the self-similar features of the Mandelbrot set at the classical Feigenbaum parameter. Maps on the unstable manifold are recalled limits of quadratic polynomials and have the maximal transcendental extension onto the complex plane. We will discuss the covering and dynamical properties of this limiting transcendental family. It will be shown, in particular, that the escaping set contains external rays, and that the Mandelbrot set is locally connected at the Feigenbaum parameter if and only if the parameter rays are realized.

http://scgp.stonybrook.edu/video_portal/video.php?id=4544

Simons- Program: Renormalization and universality in Conformal Geometry, Dynamics, Random Processes, and Field Theory