
By NTZung, on October 26th, 2014%
Here is the new version of my invited talk
“A general approach to the problem of actionangle 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
By NTZung, on October 5th, 2014%
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 CM Marle. It contains a conceptual approach to the problem of actionangle variables, with some new results (a paper is in preparation based on an old . . . → Read More: A general approach to the problem of actionangle variables
By NTZung, on May 3rd, 2012%
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)
By NTZung, on April 20th, 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)
By NTZung, on April 9th, 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 coaffine structures (that are induced from integrable systems on presymplectic manifolds) have been studied in the literature under the name”affine differential geometry”:
. . . → Read More: Actionangle variables on Dirac manifolds (2012)
By NTZung, on April 8th, 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 ReebThurston…CrainicFernandes…ScarduaSeade… to commuting foliations) ?
26/Apr/2012:
I . . . → Read More: Geometry of nonsingular integrable systems on 3manifolds (2012)
By NTZung, on April 5th, 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 2dimensional surfaces, under . . . → Read More: Geometry of integrable systems on 2D surfaces (2012)
By NTZung, on March 10th, 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 nmanifolds (2012)
By NTZung, on January 21st, 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 “nonHamiltonian” 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 nonHamiltonian systems, and show that such nondegenerate singularities . . . → Read More: Nondegenerate singularities of integrable dynamical systems (2012)
By NTZung, on January 11th, 2012%
Preprint, version 11/01/2012
Arxiv: http://arxiv.org/abs/1201.2219
Pdf file here
Abstract: In a paper with JeanPaul Dufour in 1999 \cite{DufourZungNambu1999}, 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{DufourZungNambu1999}, namely the case of smooth linearization of Nambu . . . → Read More: New results on the linearization of Nambu structures (2012)
By NTZung, on January 3rd, 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 11361179
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)
By NTZung, on January 3rd, 2012%
Entropy of geometric structures (2011)
By NTZung, on January 3rd, 2012%
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 infinitedimensional Hamiltonian system, which admits nonelliptic 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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