Name required Email will not be published required Website This blog is kept spam free by. Symplectic topology of integrable Hamiltonian systems, I: Arnold-Liouville with singularities. Makhlouf, Formality and deformation of universal enveloping algebras, International Journal of Theoretical Physics, 47 2008 , 311—332. Poisson manifolds play a fundamental role in Hamiltonian dynamics, where they serve as phase spaces. We also introduce some notions and results of the theory of Lie algebroids including related Poisson structures on the dual bundle to the Lie algebroid. The special case of spacelike leafs evolving in time is studied.
On the general position property of simple Bott integrals. If anyone is working on it, please consult with Laurent or Philipp Lohrmann who imporoved some of our quadratization results. Algebra 299 2006 , no. Poisson structures and their normal forms. On a large class of three-dimensional Hamiltonian systems.
Tang, Geometry of orbit spaces of proper Lie groupoids, arXiv:1101. Contents: Generalities on Poisson Structures; Poisson Cohomology; Levi Decomposition; Linearization of Poisson Structures; Multiplicative and Quadratic Poisson Structures; Nambu Structures and Singular Foliations; Lie Groupoids; Lie Algebroids. Responsibility: Jean-Paul Dufour, Nguyen Tien Zung. The E-mail message field is required. Hence, in the present case, the full diffeomorphism symmetry is then broken to a smaller group,. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry.
Our results solve a long-standing problem, and improve in a significant way previous results obtained by Rüssmann, Vey, Ito, Kappeler, Kodama, Nemethi, Bruno and Walcher. Even when it comes to classical results, the book gives new insights. But Nambu structures are dual to integrable differential forms, and as such they are very useful for the theory of singular foliations. Linearization of poisson structures -- 5. We sketch a geometric proof of Conn's linearizationtheorem for analytic Poisson structures witha semisimple linear part. Proceedings of the Steklov Institute of Mathematics. Even when it comes to classical results, the book gives new insights.
We also show that this framework can be applied to the more general context of Lie algebroids. In particular, we give a classification of linear Nambu structures also called finitedimensional Nambu-Lie algebras , and a linearization of Nambu tensors and co-Nambu forms, under the nondegeneracy condition. Papers from undergraduate period: with Lada Polyakova A topological classification of integrable geodesic flows on the two-dimensional sphere with an additional integral quadratic in the momenta. Lie Theory 19 2009 , no. The proof is based on Reeb stability for singular foliation, Moser trick, and the geometric approximation method developed in our papers on normal forms of vector fields.
Compatible contact structures for integrable Hamiltonian systems. Generalities on poisson structures -- 2. We have also argued that the constraints 2. Unterberger, Supersymmetric extension of Schrodinger-invariance, Nuclear Physics B, vol. The usefulness of Nambu structures in physics is rather dubious. The authors take a novel approach, using the techniques of symplectic geometry.
Physics, 33 1995 , 187-193. Blaise Pascal 13 2006 , no. Kolmogorov condition for integrable systems with focus-focus singularities. Metacurvature of Riemannian Poisson-Lie groups. After the publication of the book, there have been new interesting results about normal forms of Poisson structures, including: Crainic, Fernandes, Martinez geometric approach to linearization of Poisson structures and groupoids, Poisson structures of compact type , Marcut, Vorobiev normal forms in a neighborhood of a symplectic leaf , Stolovitch and Lohrmann analytic and Gevrey-class normal forms , Monnier, Miranda and myself rigidity of Hamiltonian actions , and so on.