A Priori Bounds for Quadratic Maps
Mikhail Lyubich (State University of New York, Stony Brook)
"A priori bounds" provide us with a uniform geometric control of dynamical systems in all scales. Central problems of Holomorphic Dynamics, like universal self-similarity of dynamical and parameter pictures, MLC, topological structure of neutral maps, and the area problem for Julia sets, depend on such bounds. We will give an overview of advances in this problem over the past 30 years.