Date: Friday, February 01, 2013
Location: 3096 East Hall (3:00 PM to 4:00 PM)
Title: Absolute continuity, exponents, and rigidity
Abstract: The geodesics in a compact surface of negative curvature
display stability properties originating in the chaotic, hyperbolic
nature of the geodesic flow on the associated unit tangent bundle.
Considered as a foliation of this bundle, this collection of geodesics
persists in a strong way when one perturbs of the Riemannian metric,
or the geodesic flow generated by this metric, or even the time-one
map of this flow: for any perturbed system there is a corresponding
"shadow foliation" with one-dimensional smooth leaves that is
homeomorphic to the original geodesic foliation. A counterpart to
this foliation stability is a curious rigidity phenomenon that arises
when one studies the disintegration of volume along the leaves of this
perturbed shadow foliation. I will describe this phenomenon and its
underlying causes. This is recent work with Artur Avila and Marcelo
Viana.
Speaker: Amie Wilkinson
Institution: University of Chicago
Event Organizer: Spatzier
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