BIRS Workshop Lecture Videos

Banff International Research Station Logo

BIRS Workshop Lecture Videos

Some properties of hyperbolic dynamics from micro-local analysis Faure, Frederic


In hyperbolic dynamics (Anosov dynamics) each trajectory is strongly unstable and its behavior is unpredictable. A smooth probability distribution evolves also in a complicated way since it acquires higher and higher oscillations. Nevertheless using micro-local analysis, this evolution is predictable in the sense of distributions. It is similar to a quantum scattering problem in cotangent space as treated by Helffer and Sjöstrand using escape functions in (86'). In this talk we will use wave-packet transform (or FBI transform) and explain how to derive some spectral properties of the dynamics, as the existence of the intrinsic discrete spectrum of Ruelle resonances, a fractal Weyl law, estimates on the wave front set of the resonances, and band structure in the case of geodesic flow. Collaboration with Masato Tsujii.

Item Media

Item Citations and Data


Attribution-NonCommercial-NoDerivatives 4.0 International