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Microlocal analysis of contact Anosov flows

Recent developments in microlocal analysis October 14, 2019 - October 18, 2019

October 18, 2019 (09:00 AM PDT - 10:00 AM PDT)
Speaker(s): Frederic Faure (Université Grenoble Alpes (Université de Grenoble I - Joseph Fourier))
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Abstract

In the 80's, D. Ruelle, D. Bowen and others have introduced probabilistic and spectral methods in order to study deterministic chaos ("Ruelle resonances"). For example, a geodesic flow on a strictly negative curvature Riemannian manifold is chaotic:  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 this evolution is predictable in the sense of distributions and converges towards equilibrium. Following this approach and use of microlocal analysis, one obtains that long time fluctuations of classical probabilities are described by an effective quantum wave equation. This may be surprising because there is no added quantization procedure. Joint work with Masato Tsujii.

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