Lyapunov exponent of random dynamical systems on the circle

CDSNS Colloquium
Friday, March 12, 2021 - 1:00pm for 1 hour (actually 50 minutes)
Zoom (see add'l notes for link)
Dominique Malicet – University Paris-Est Marne la vallée – dominique.malicet@univ-eiffel.fr
Alex Blumenthal

Please Note: Zoom link:

We consider a sequence of compositions of orientation preserving diffeomorphisms of the circle chosen randomly with a fixed distribution law. There is naturally associated a Lyapunov exponent, which measures the rate of exponential contractions of the sequence. It is known that under some assumptions, if this Lyapunov exponent is null then all the diffeomorphisms are simultaneously conjugated to rotations. If the Lyapunov exponent is not null but close to 0, we study how well we can approach rotations by a simultaneous conjugation. In particular, our results can apply to random products of matrices 2x2, giving quantitative versions of the classical Furstenberg theorem.