Seminar

On a limit set of analytic endomorphism one can consider 3 natural measures:
Hausdorff measure, maximal entropy measure, and harmonic measure. Rigidity theorems
sate that if two of these 3 measures coincide, then the dynamical system must be very 
specific.This is the general belief, but it is still open in the case of the pair: 
harmonic measure and Hausdorff measure.The difficulty lies in a certain quite
naturally looking free boundary problem, which will be described.