School of Mathematics Seminars and Lectures
`Combining Fuchsian reflection groups and quadratic polynomial dynamics (after Lee, Lyubich, Makarov and Mukherjee)'
by Prof. Mahan Mj (TIFR, Mumbai)
Wednesday, January 9, 2019
from
to
(Asia/Kolkata)
at A-369
at A-369
Description |
Abstract: Two fundamentally different kinds of holomorphic dynamical systems exist on the Riemann sphere: 1) Fuchsian or more generally Kleinian groups 2) Iteration of polynomials or rational maps. They have been studied for more than a century starting with Poincare, Fatou and Julia amongst others. A dictionary between the fundamental structures of these two kinds of dynamical systems was brought into focus by Sullivan in the 80's and subsequently by McMullen. However a common framework for dealing with both is lacking. A couple of recent papers by Lee, Lyubich, Makarov and Mukherjee changes that and provides a natural class of examples where Fuchsian reflection groups on the one hand are combined with the dynamics of $z \to z^2 +c$ on the other. This will be an expository talk where we shall first describe the dictionary, say what is meant by combining dynamical systems and conclude with a description of the results of the authors. |