Colloquium: Zohovitzki prize lecture - Ariel Rapaport, "Self-affine measures with equal Hausdorff and Lyapunov dimensions"

Thu, 22/06/201714:30-15:30
Manchester Building (Hall 2), Hebrew University Jerusalem
A measure on the plane is called self-affine if it is stationary with respect to a finitely supported measure on the affine group of R^2. Under certain randomization, it is known that the Hausdorff dimension of these measures is almost surely equal to the Lyapunov dimension, which is a quantity defined in terms of the linear parts of the affine maps. I will present a result which provides conditions for equality between these two dimensions, and connects the theory of random matrix products with the dimension of self-affine measures.