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# Documents  Dyatlov, Semyon | enregistrements trouvés : 2

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## A microlocal toolbox for hyperbolic dynamics Dyatlov, Semyon | CIRM H

Post-edited

Research talks;Partial Differential Equations;Dynamical Systems and Ordinary Differential Equations;Geometry

I will discuss recent applications of microlocal analysis to the study of hyperbolic flows, including geodesic flows on negatively curved manifolds. The key idea is to view the equation $(X + \lambda)u = f$ , where $X$ is the generator of the flow, as a scattering problem. The role of spatial infinity is taken by the infinity in the frequency space. We will concentrate on the case of noncompact manifolds, featuring a delicate interplay between shift to higher frequencies and escaping in the physical space. I will show meromorphic continuation of the resolvent of $X$; the poles, known as Pollicott-Ruelle resonances, describe exponential decay of correlations. As an application, I will prove that the Ruelle zeta function continues meromorphically for flows on non-compact manifolds (the compact case, known as Smale's conjecture, was recently settled by Giulietti-Liverani- Pollicott and a simple microlocal proof was given by Zworski and the speaker). Joint work with Colin Guillarmou. I will discuss recent applications of microlocal analysis to the study of hyperbolic flows, including geodesic flows on negatively curved manifolds. The key idea is to view the equation $(X + \lambda)u = f$ , where $X$ is the generator of the flow, as a scattering problem. The role of spatial infinity is taken by the infinity in the frequency space. We will concentrate on the case of noncompact manifolds, featuring a delicate interplay between ...

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## Mathematical theory of scattering resonances Dyatlov, Semyon ; Zworski , Maciej | American Mathematical Society 2019

Ouvrage

- xi; 634 p.
ISBN 978-1-4704-4366-5

Graduate studies in mathematics , 0200

Localisation : Collection 1er étage

résonance # dispersion # oscillation # fréquence des oscillations # physique mathématique # prolongement méromorphe # théorie spectrale # valeurs propres # théorie quantique

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