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Perturbation results for a class of singular Hamiltonian systems

Antonio Ambrosetti, Ivar Ekeland (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The existence of solutions with prescribed period T for a class of Hamiltonian systems with a Keplerian singularity is discussed.

Poincaré inequalities and Sobolev spaces.

Paul MacManus (2002)

Publicacions Matemàtiques

Our understanding of the interplay between Poincaré inequalities, Sobolev inequalities and the geometry of the underlying space has changed considerably in recent years. These changes have simultaneously provided new insights into the classical theory and allowed much of that theory to be extended to a wide variety of different settings. This paper reviews some of these new results and techniques and concludes with an example on the preservation of Sobolev spaces by the maximal function.[Proceedings...

Poisson cohomology of regular Poisson manifolds

Ping Xu (1992)

Annales de l'institut Fourier

The main purpose of this paper is to suggest a method of computing Poisson cohomology of a Poisson manifold by means of symplectic groupoids. The key idea is to convert the problem of computing Poisson cohomology to that of computing de Rham cohomology of certain manifolds. In particular, we shall derive an explicit formula for the Poisson cohomology of a regular Poisson manifold where the symplectic foliation is a trivial fibration.

Poisson Lie groups and their relations to quantum groups

Janusz Grabowski (1995)

Banach Center Publications

The notion of Poisson Lie group (sometimes called Poisson Drinfel'd group) was first introduced by Drinfel'd [1] and studied by Semenov-Tian-Shansky [7] to understand the Hamiltonian structure of the group of dressing transformations of a completely integrable system. The Poisson Lie groups play an important role in the mathematical theories of quantization and in nonlinear integrable equations. The aim of our lecture is to point out the naturality of this notion and to present basic facts about...

Poisson structures on certain moduli spaces for bundles on a surface

Johannes Huebschmann (1995)

Annales de l'institut Fourier

Let Σ be a closed surface, G a compact Lie group, with Lie algebra g , and ξ : P → Σ a principal G -bundle. In earlier work we have shown that the moduli space N ( ξ ) of central Yang-Mills connections, with reference to appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yields a homeomorphism from N ( ξ ) onto a certain representation space Rep ξ ( Γ , G ) , in fact a diffeomorphism, with reference to suitable smooth structures C ∞ ( N ( ξ ) ) and C ∞ Rep ξ ( Γ , G ) , where Γ denotes the universal central extension of...

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