KTH/SU Mathematics Colloquium
March 4, 2009
Viviane Baladi, Ecole Normale Supérieure, Paris
Statistical properties of piecewise hyperbolic systems
such as billiards: new-old tools from analysis
Strong ergodic properties (such as exponential mixing)
have been proved for various smooth dynamical systems by
first obtaining a spectral gap for a suitable
"transfer" operator acting on an appropriate Banach space.
Some natural dynamical systems, such as
billiards, are only piecewise smooth, and this poses
serious technical problems. I will try to explain
recent joint work with Sebastien Gouezel, in which we
show that classical tools such as complex interpolation
on anisotropic Sobolev-Triebel spaces, and an old result of
Strichartz on Fourier multipliers, can solve
those problems. I will also briefly discuss recent improvements.
(Work together with Gouezel, Balint, Liverani.)