Rudolph's theorem on the Furstenberg conjecture

Joachim Cuntz (University of Muenster)

Tuesday 5th March, 2013 16:00-17:00 Maths 203

Abstract

Rudolph's theorem states: Let p and q be two natural numbers which are relatively prime. 
Assume that $ \mu $ is a measure on the unit interval which is invariant and ergodic for the 
two transformations given by multiplication by p and q mod 1. If $ \mu $ is not Lebesgue 
measure, then both transformations have entropy 0 with respect to $ \mu $. We try to sketch 
a proof of this theorem.

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