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Here is the new version of my invited talk “A general approach to the problem of action-angle variables” (PDF File: AATalk2014, version 26/10/2014) to be presented et the conference in honour of Charles Michel Marle’s 70th birthday in November 2014 in Paris. Here is the website of the conference: http://www.imcce.fr/Equipes/ASD/person/albouy/Marle2014.html
These are the slides (preliminary version, to be revised) for a talk that I’ll give in Paris (24/11/2014) in the Conference in honour of the 80th birthday of C-M Marle. It contains a conceptual approach to the problem of action-angle variables, with some new results (a paper is in preparation based on an old . . . → Read More: A general approach to the problem of action-angle variables 03/June/2012 I just modified the text a bit and submitted it on arxiv PDF File. 08/May/2012 A preliminary working version is available here: PDF File. 10 pages. Wrote down the results in the regular case. Will probably add a section about singularities to make this note more substantial. 07/May/2012 8 pages (9 pages by . . . → Read More: A note on commuting foliations (2012) 24/Apr/2012 15h20: The first version of this paper is now available: Orbital linearization of smooth completely integrable vector fields (Click on the above link for the PDF file) Abstract: The main purpose of this note is to prove the smooth local orbital linearization theorem for smooth vector fields which admit a complete set of . . . → Read More: Orbital linearization of smooth completely integrable vector fields (2012) 18/Apr/2012: Arxiv: http://arxiv.org/abs/1204.3865 I finally submitted this paper to the journal Geometry & Topology. Corrections to the first version: * One of the word “contravariant” should be changed to “covariant” * The co-affine structures (that are induced from integrable systems on presymplectic manifolds) have been studied in the literature under the name”affine differential geometry”: . . . → Read More: Action-angle variables on Dirac manifolds (2012) 28/Apr/2012 This 3D project is not prioritary, so I’ll postpone it until I’m out of other ideas :-) Need to work on something more exciting, or I’ll feel bored and tired. Right now maybe I’ll write up some stuff about stability of commuting singular foliations (extenstion of Reeb-Thurston-…-Crainic-Fernandes-…-Scardua-Seade-… to commuting foliations) ? 26/Apr/2012: I . . . → Read More: Geometry of nonsingular integrable systems on 3-manifolds (2012) The first version of this paper is now finished. Here is the PDF file. NT Zung & NV Minh, Geometry of integrable systems on 2D surfaces Abstract: This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under . . . → Read More: Geometry of integrable systems on 2D surfaces (2012) Updated 17/03/2013: this paper has been accepted for publications in J. Math. Soc. Japan, after a small revision. Apparently it has also been cited in a recent work by Ishida: arxiv.org/pdf/1302.0633 Updated 18/03/2012: 2nd version, which corrects a series of misprints and imprecisions in the 1st version. After two months of intensive work, we . . . → Read More: Geometry of R^n actions on n-manifolds (2012) Last updated: 14/March/2012 I have now updated my preprint “Nondegenerate singularities of integrable dynamical systems”. I’ve also changed the title a bit, from “non-Hamiltonian” to “dynamical”. PDF file: Nondegenerate_V2_2012.pdf Preprint on Arxiv: http://arxiv.org/abs/1108.3551 ABSTRACT: We give a natural notion of nondegeneracy for singular points of integrable non-Hamiltonian systems, and show that such nondegenerate singularities . . . → Read More: Nondegenerate singularities of integrable dynamical systems (2012) Preprint, version 11/01/2012 Arxiv: http://arxiv.org/abs/1201.2219 Pdf file here Abstract: In a paper with Jean-Paul Dufour in 1999 \cite{DufourZung-Nambu1999}, we gave a classification of linear Nambu structures, and obtained linearization results for Nambu structures with a nondegenerate linear part. There was a case left open in \cite{DufourZung-Nambu1999}, namely the case of smooth linearization of Nambu . . . → Read More: New results on the linearization of Nambu structures (2012) (with E Miranda and Ph Monnier) Rigidity of Hamiltonian ations on Poisson manifolds , Advances in Mathematics, Volume 229, Issue 2, 30 January 2012, Pages 1136-1179 Arxiv: http://arxiv.org/abs/1102.0175 ScienceDirect: http://www.sciencedirect.com/science/article/pii/S0001870811003574 It took us several years to write up this paper, because although we “always knew” that the rigidity result was true for Hamiltonian actions . . . → Read More: Rigidity of Hamiltonian ations on Poisson manifolds (2012) Entropy of geometric structures (2011) My only paper on PDEs so far: (With Th. Kappeler, P. Topalov, P. Lohrmann) Birkhoff coordinates for the focusing NLS equation. Comm. Math. Phys. 285 (2009), no. 3, 1087–1107 The system in question is an infinite-dimensional Hamiltonian system, which admits non-elliptic singularities. But near 0 the singularity is elliptic, and it admits a local . . . → Read More: Nonlinear Schrodinger equation: focusing case (2009) |
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