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Documents  37C30 | enregistrements trouvés : 25

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Research talks;Lie Theory and Generalizations;Number Theory

We discuss the distribution of the trace of a random matrix in the compact Lie group USp2g, with the normalized Haar measure. According to the generalized Sato-Tate conjecture, if A is an abelian variety of dimension g defined over the rationals, the sequence of traces of Frobenius in the successive reductions of A modulo primes appears to be equidistributed with respect to this distribution. If g = 2, we provide expressions for the characteristic function, the density, and the repartition function of this distribution in terms of higher transcendental functions, namely Legendre and Meijer functions. We discuss the distribution of the trace of a random matrix in the compact Lie group USp2g, with the normalized Haar measure. According to the generalized Sato-Tate conjecture, if A is an abelian variety of dimension g defined over the rationals, the sequence of traces of Frobenius in the successive reductions of A modulo primes appears to be equidistributed with respect to this distribution. If g = 2, we provide expressions for the cha...

11G05 ; 11G10 ; 14G10 ; 37C30

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- 638 p.
ISBN 978-3-540-23189-9

Localisation : Colloque 1er étage (HOUC)

théorie des nombres # fraction continue # théorie métrique # matrice aléatoire # fonction zêta # système dynamique # orbite périodique de champs de vecteurs # géométrie non-commutative # chaos quantique

11A55 ; 11K50 ; 11M41 ; 15A52 ; 37C27 ; 37C30 ; 58B34 ; 81Q50 ; 81R60

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- xii; 342 p.
ISBN 978-0-8218-4269-0

Contemporary mathematics , 0484

Localisation : Collection 1er étage

géométrie spectrale # théorie des nombres # formule des traces # problème isospectrale # fonction zéta # ergodicité quantique # onde aléatoire # analyse géométrique discrète

58J50 ; 11M36 ; 37C30 ; 35P05 ; 60J60

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

We consider the one-parameter families of transfer operators for geodesic flows on negatively curved manifolds. We show that the spectra of the generators have some "band structure" parallel to the imaginary axis. As a special case of "semi-classical" transfer operator, we see that the eigenvalues concentrate around the imaginary axis with some gap on the both sides.

37C30 ; 37D40 ; 53D25 ; 81Q50

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Research talks;Partial Differential Equations;Dynamical Systems and Ordinary Differential Equations;Mathematical Physics

Hyperbolic (Anosov or Axiom A) flows have discrete Ruelle spectrum. For contact Anosov flows, e.g. geodesic flows, where a smooth contact one form is preserved, the trapped set is a smooth symplectic manifold, normally hyperbolic, and M. Tsujii, S. Nonnenmacher and M. Zworski, have given an estimate for the asymptotic spectral gap, i.e. that appears in the limit of high frequencies in the flow direction. We will propose a different approach that may improve this estimate. This will be presented on a simple toy model, partially expanding maps. Work with Tobias Weich. Hyperbolic (Anosov or Axiom A) flows have discrete Ruelle spectrum. For contact Anosov flows, e.g. geodesic flows, where a smooth contact one form is preserved, the trapped set is a smooth symplectic manifold, normally hyperbolic, and M. Tsujii, S. Nonnenmacher and M. Zworski, have given an estimate for the asymptotic spectral gap, i.e. that appears in the limit of high frequencies in the flow direction. We will propose a different approach that ...

37C30 ; 37D20 ; 58J50

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Research talks;Dynamical Systems and Ordinary Differential Equations;Geometry;Number Theory

Given the Apollonian Circle packing, or something similar, one can consider the distribution of the logarithms of the radii. These can be shown to satisfy a Central Limit Theorem. The method of proof uses iterated function schemes and transfer operators and has applications to other conformal dynamical systems.

52C26 ; 37C30 ; 11K55 ; 37F35 ; 37D35

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Research talks;Dynamical Systems and Ordinary Differential Equations;Probability and Statistics

I will discuss the simplest possible (non trivial) example of a fast-slow partially hyperbolic system with particular emphasis on the problem of establishing its statistical properties.

37A25 ; 37C30 ; 37D30 ; 37A50 ; 60F17

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Research talks;Partial Differential Equations;Number Theory;Mathematical Physics

Over the last few years I developed (partly jointly with coauthors) dual 'slow/fast' transfer operator approaches to automorphic functions, resonances, and Selberg zeta functions for certain hyperbolic surfaces/orbifolds L \ H with cusps (both of finite and infinite area; arithmetic and non-arithmetic).
Both types of transfer operators arise from discretizations of the geodesic flow on L \ H. The eigenfunctions with eigenvalue 1 of slow transfer operators characterize Maass cusp forms. Conjecturally, this characterization extends to more general automorphic functions as well as to residues at resonances. The Fredholm determinant of the fast transfer operators equals the Selberg zeta function, which yields that the zeros of the Selberg zeta function (among which are the resonances) are determined by the eigenfunctions with eigenvalue 1 of the fast transfer operators. It is a natural question how the eigenspaces of these two types of transfer operators are related to each other.
Over the last few years I developed (partly jointly with coauthors) dual 'slow/fast' transfer operator approaches to automorphic functions, resonances, and Selberg zeta functions for certain hyperbolic surfaces/orbifolds L \ H with cusps (both of finite and infinite area; arithmetic and non-arithmetic).
Both types of transfer operators arise from discretizations of the geodesic flow on L \ H. The eigenfunctions with eigenvalue 1 of slow transfer ...

37C30 ; 11F03 ; 37D40

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Research schools

We will discuss an approach to the statistical properties of two-dimensional dispersive billiards (mostly discrete-time) using transfer operators acting on anisotropic Banach spaces of distributions. The focus of this part will be our recent work with Mark Demers on the measure of maximal entropy but we will also survey previous results by Demers, Zhang, Liverani, etc on the SRB measure.

37D50 ; 37C30 ; 37B40

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Research schools

We will discuss an approach to the statistical properties of two-dimensional dispersive billiards (mostly discrete-time) using transfer operators acting on anisotropic Banach spaces of distributions. The focus of this part will be our recent work with Mark Demers on the measure of maximal entropy but we will also survey previous results by Demers, Zhang, Liverani, etc on the SRB measure.

37D50 ; 37C30 ; 37B40

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Research schools

We will discuss an approach to the statistical properties of two-dimensional dispersive billiards (mostly discrete-time) using transfer operators acting on anisotropic Banach spaces of distributions. The focus of this part will be our recent work with Mark Demers on the measure of maximal entropy but we will also survey previous results by Demers, Zhang, Liverani, etc on the SRB measure.

37D50 ; 37C30 ; 37B40

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Research schools

We present a functional-analytic approach to the study of transfer operators for Anosov flows. To study transfer operators, a basic idea in semi-classical analysis suggests to look at the action of the flow on the cotangent bundle. Though this idea is simple and intuitive (as we will explain in the lectures), we need some framework to make it work. In the lectures, we present such a framework based on a wave-packet transform.

37D20 ; 37C30

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Research schools

We present a functional-analytic approach to the study of transfer operators for Anosov flows. To study transfer operators, a basic idea in semi-classical analysis suggests to look at the action of the flow on the cotangent bundle. Though this idea is simple and intuitive (as we will explain in the lectures), we need some framework to make it work. In the lectures, we present such a framework based on a wave-packet transform.

37D20 ; 37C30

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Research schools

We present a functional-analytic approach to the study of transfer operators for Anosov flows. To study transfer operators, a basic idea in semi-classical analysis suggests to look at the action of the flow on the cotangent bundle. Though this idea is simple and intuitive (as we will explain in the lectures), we need some framework to make it work. In the lectures, we present such a framework based on a wave-packet transform.

37D20 ; 37C30

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- 314 p.
ISBN 978-981-02-3328-0

Advanced series in nonlinear dynamics , 0016

Localisation : Ouvrage RdC (BALA)

opérateur de Perron-Frobenius # décroissance des corrélations # dynamique hypberbolique # dynamique expansive # fonction zêta dynamique # application de l'interval # mesure SRB # tour de Young

37C30 ; 37-02 ; 47B38 ; 37D20 ; 37A25

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- 495 p.
ISBN 978-0-521-55124-3

Localisation : Ouvrage RdC (LIND)

système dynamique # dynamique symbolique # sous-shifts de type fini # système sofique # entropie # codage # classification des sous-shifts de type fini

37B10 ; 15A48 ; 37BXX ; 54H20 ; 94A24 ; 94B60 ; 37C30

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- 211 p.
ISBN 978-1-85233-125-2

Universitext

Localisation : Ouvrage RdC (EVER)

géométrie algébrique # mesure # système dynamique différentiable # courbe elliptique # entropie # arithmétique # mesure de Mordell

11G50 ; 11C08 ; 11G07 ; 37A45 ; 37B40 ; 37C30 ; 54H20

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- 136 p.
ISBN 978-0-8218-3833-4

University lecture series , 0036

Localisation : Collection 1er étage

géométrie non-commutative # théorie quantique des champs # espace temps courbé # système dynamique non-commutatif # variété arithmétique # k-théorie # c*algèbre # frontière non-commutative # mécanique statistique quantique # théorie de Galois # surface arithmétique # géométrie d'Arakelov # cohomologie d'Archimède

58B34 ; 58-02 ; 81T75 ; 83C47 ; 46L55 ; 37C30 ; 14G40 ; 11G35

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- 138 p.
ISBN 978-3-540-40121-6

Springer monographs in mathematics

Localisation : Ouvrage RdC (MARG)

système dynamique # courbure négative # fonction zéta # opérateur de transfert # orbite périodique # système d'Anosov # flot hyperbolique

37A05 ; 35A10 ; 37B10 ; 37C10 ; 37C27 ; 37C30 ; 37C35 ; 37C40 ; 37D20 ; 37D35 ; 37D40

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- v; 60 p.
ISBN 978-0-8218-7290-1

Memoirs of the american mathematical society , 1037

Localisation : Collection 1er étage

fonction zêta # modèle d'Ising

37B50 ; 37B10 ; 37C30 ; 82B20 ; 11M41

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