Séminaires : Phd Seminar - Séminaire des doctorant.e.s

Equipe(s) : doctorants,
Responsables :Salim Alloun, Pedro Alves, Baptiste Dugué, Brian Flanagan, Ivory Fronteau, Kostyantyn Krutoy
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Description

Le séminaire des doctorant.e.s est l'occasion pour les doctorant.e.s de présenter des résultats et des problématiques dignes d'intérêt devant un public de non-spécialistes. L'ambiance y est informelle ; poser des questions naïves est encouragé, et les questions moins naïves sont bienvenues dans la mesure où elles n'entravent pas le bon déroulement de l'exposé.

Chaque jeudi à 18h, en alternance entre Jussieu et Sophie Germain.

The PhD seminar is an opportnuity for PhD students to present results and topics worthy of interest in front of a non-specialist audience. The mood is informal ; asking naive questions is highly encouraged and less naive questions are also welcomed, as long as they don't intefere with the smoothness of the talk.

Every Thursday at 6pm, alternating between Jussieu and Sophie Germain.

Orateur(s) Alexander Adam - ,
Titre Resonances for Anosov diffeomorphisms
Date19/01/2017
Horaire18:00 à 19:00
Diffusion
Résume Deterministic chaotic behavior of invertible maps $T$ is appropriately described by the existence of expanding and contracting directions for the differential of $T$. A special class of such maps are Anosov diffeomorphisms. A famous example of such a diffeomorphism on the $2$-torus is induced by the matrix $M=\begin{pmatrix}2&1\\1&1\end{pmatrix}$. For all pairs of $L_2$-functions, real-analytic on the $2$-torus, one defines a correlation function for $T$ which captures the independence of such a pair under the evolution $T^n$ as $n\to\infty$. What is the rate of convergence of the correlation as $n\to\infty$, e.g. how fast is the mixing of $T$? The behavior of the correlation for $M$ is well-understood. In this talk I consider small perturbations $T$ of $M$. The composition operator $\mathcal{K}g:=g\circ T$, acting on a suitable Hilbert space, allows us to study the correlation from a functional analytic point of view. The eigenvalues of $\mathcal{K}$ are related to the zeros - the Ruelle resonances - of the analytically continued dynamical determinant of $T$. The trivial resonance is $1$ and it is the only one for $M$. The existence of a non-trivial resonance would change the speed of mixing drastically. For the considered perturbations at least one non-trivial resonance of $T$ appears.
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