Currently, he is a Professor of Mathematics at
Stony Brook University and the Director of the Institute of Mathematical Sciences at Stony Brook. From 2002-2008, he also held a position of Canada Research Chair at the
University of Toronto. He is credited with several important contributions to the study of
dynamical systems. In his 1984 Ph.D. thesis, he proved fundamental results on
ergodic theory and the structural stability of
rational mapping. Due to this work, the measure of maximal
entropy of a rational map (the
Mané-Lyubich measure) bears his name. In 1999, he published the first non-numerical proof of the
universality of the
Feigenbaum constants in chaos theory. He received the 2010
Jeffery–Williams Prize from the
Canadian Mathematical Society. In 2012, he became a fellow of the
American Mathematical Society. He was selected as one of the plenary speakers for the 2014
ICM in
Seoul. ==Notes==