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# Documents  58J51 | enregistrements trouvés : 7

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## Nodal lines and domains for Eisenstein series on surfaces Naud, Frédéric | CIRM H

Multi angle

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

Eisenstein series are the natural analog of ”plane waves” for hyperbolic manifolds of infinite volume. These non-$L^2$ eigenfunctions of the Laplacian parametrize the continuous spectrum. In this talk we will discuss the structure of nodal sets and domains for surfaces. Upper and lower bounds on the number of intersections of nodal lines with ”generic” real analytic curves will be given, together with similar bounds on the number of nodal domains inside the convex core. The results are based on equidistribution theorems for restriction of Eisenstein series to curves that bear some similarity with the so-called ”QER” results for compact manifolds. Eisenstein series are the natural analog of ”plane waves” for hyperbolic manifolds of infinite volume. These non-$L^2$ eigenfunctions of the Laplacian parametrize the continuous spectrum. In this talk we will discuss the structure of nodal sets and domains for surfaces. Upper and lower bounds on the number of intersections of nodal lines with ”generic” real analytic curves will be given, together with similar bounds on the number of nodal ...

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## Correlation spectrum of Morse-Smale flows Rivière, Gabriel | CIRM H

Multi angle

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

I will explain how one can get a complete description of the correlation spectrum of a Morse-Smale flow in terms of the Lyapunov exponents and of the periods of the flow. I will also discuss the relation of these results with differential topology.
This a joint work with Nguyen Viet Dang (Université Lyon 1).

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## Delocalization of eigenfunctions and quantum chaos - lecture 1 Anantharaman, Nalini | CIRM H

Multi angle

Ecoles de recherche;Algebra;Combinatorics

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## Delocalization of eigenfunctions and quantum chaos - lecture 2 Anantharaman, Nalini | CIRM H

Multi angle

Ecoles de recherche;Algebra;Combinatorics

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## Delocalization of eigenfunctions and quantum chaos - lecture 3 Anantharaman, Nalini | CIRM H

Multi angle

Ecoles de recherche;Algebra;Combinatorics

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## Semiclassical behaviour of quantum eigenstates - lecture 1 Rivière, Gabriel | CIRM H

Multi angle

Research school;Dynamical Systems and Ordinary Differential Equations;Mathematical Physics

Given a quantum Hamiltonian, I will explain how the dynamical properties of the underlying classical Hamiltonian affect the behaviour of quantum eigenstates in the semiclassical limit. I will mostly focus on two opposite dynamical paradigms: completely integrable systems and chaotic ones. I will introduce tools from microlocal analysis and show how to use them in order to illustrate the classical-quantum correspondance and to compare properties of completely integrable and chaotic systems. Given a quantum Hamiltonian, I will explain how the dynamical properties of the underlying classical Hamiltonian affect the behaviour of quantum eigenstates in the semiclassical limit. I will mostly focus on two opposite dynamical paradigms: completely integrable systems and chaotic ones. I will introduce tools from microlocal analysis and show how to use them in order to illustrate the classical-quantum correspondance and to compare properties ...

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## Semiclassical behaviour of quantum eigenstates - lecture 2 Rivière, Gabriel | CIRM H

Multi angle

Research school;Dynamical Systems and Ordinary Differential Equations;Mathematical Physics

Given a quantum Hamiltonian, I will explain how the dynamical properties of the underlying classical Hamiltonian affect the behaviour of quantum eigenstates in the semiclassical limit. I will mostly focus on two opposite dynamical paradigms: completely integrable systems and chaotic ones. I will introduce tools from microlocal analysis and show how to use them in order to illustrate the classical-quantum correspondance and to compare properties of completely integrable and chaotic systems. Given a quantum Hamiltonian, I will explain how the dynamical properties of the underlying classical Hamiltonian affect the behaviour of quantum eigenstates in the semiclassical limit. I will mostly focus on two opposite dynamical paradigms: completely integrable systems and chaotic ones. I will introduce tools from microlocal analysis and show how to use them in order to illustrate the classical-quantum correspondance and to compare properties ...

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