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The symbol of a function of a pseudo-differential operator

Alfonso Gracia-saz (2005)

Annales de l'institut Fourier

We give an explicit formula for the symbol of a function of an operator. Given a pseudo-differential operator A ^ on L 2 ( ℝ N ) with symbol A ∈ 𝒞 ∞ ( T * ℝ N ) and a smooth function f , we obtain the symbol of f ( A ^ ) in terms of A . As an application, Bohr-Sommerfeld quantization rules are explicitly calculated at order 4 in ℏ .

The Weil algebra and the Van Est isomorphism

Camilo Arias Abad, Marius Crainic (2011)

Annales de l’institut Fourier

This paper belongs to a series of papers devoted to the study of the cohomology of classifying spaces. Generalizing the Weil algebra of a Lie algebra and Kalkman’s BRST model, here we introduce the Weil algebra W ( A ) associated to any Lie algebroid A . We then show that this Weil algebra is related to the Bott-Shulman complex (computing the cohomology of the classifying space) via a Van Est map and we prove a Van Est isomorphism theorem. As application, we generalize and find a simpler more conceptual...

Three results on the regularity of the curves that are invariant by an exact symplectic twist map

M.-C. Arnaud (2009)

Publications Mathématiques de l'IHÉS

A theorem due to G. D. Birkhoff states that every essential curve which is invariant under a symplectic twist map of the annulus is the graph of a Lipschitz map. We prove: if the graph of a Lipschitz map h:T→R is invariant under a symplectic twist map, then h is a little bit more regular than simply Lipschitz (Theorem 1); we deduce that there exists a Lipschitz map h:T→R whose graph is invariant under no symplectic twist map (Corollary 2).Assuming that the dynamic of a twist map restricted to a...

Through the analytic halo: Fission via irregular singularities

Philip Boalch (2009)

Annales de l’institut Fourier

This article is concerned with moduli spaces of connections on bundles on Riemann surfaces, where the structure group of the bundle may vary in different regions of the surface. Here we will describe such moduli spaces as complex symplectic manifolds, generalising the complex character varieties of Riemann surfaces.

Topologie du feuilletage fortement stable

Françoise Dal'bo (2000)

Annales de l'institut Fourier

Soient X une variété de Hadamard de courbure ≤ - 1 et Γ un groupe d’isométries non élémentaire. Nous montrons qu’il y a équivalence entre la non-arithméticité du spectre des longueurs de Γ ∖ X , le mélange topologique du flot géodésique et l’existence d’une feuille dense pour le feuilletage fortement stable.

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