2017
Dec
05

# Dynamics Seminar: Micheal Hochman (HUJI): Dimension of self-affine sets and measures

2:15pm to 3:15pm

## Location:

Ross 70

I will discuss joint work with Balazs Barany and Ariel Rapaport on the dimension of self-affine sets and measures. We confirm that under mild irreducibility conditions on the generating maps, the dimension is "as expected", i.e. equal to the affinity or Lyapunov dimension. This completes a program started by Falconer in the 1980s. In the first part of the talk I will explain how the Lyapunov dimension arises from Ledrappier-Young formula for self-affine sets, and then explain how additive combinatorics methods can be used to prove that this is the correct dimension.