We’re fools whether we dance or not, so we might as well dance.
by Japanese Proverb

Integrable p-vector fields and singular foliations

There seems to be a lot of confusion (among my colleagues, and also of myself) concerning the relationships between singular foliations and integrable p-vector fields (a.k.a. Nambu structures). The aim of this note is to make some clarifications.

1) How to construct a singular foliation from an integrable p-vector field ?

The obvious (but . . . → Read More: Integrable p-vector fields and singular foliations

Talk at AlanFest 07/2013


This week I’m at the AlanFest in EPFL, Switzerland, on the occasion of Alan Weinstein’s 70th birthday. I gave  a talk on Thursday entitled:

A normalization toolbox, with applications to singular foliations

Here are the slides of my talks (with some typographical errors), for people who might be interested:


. . . → Read More: Talk at AlanFest 07/2013

Linearization of smooth integrable systems

I’m writing down here the ideas for proving that smooth nondegenerate integrable dynamical systems are smoothly linearizable. The analytic case can be proved using analytic torus actions (my paper about that will appear in Ergodic Th Dyn Sys). I think the smooth case is also true, but the proof is much more complicated than . . . → Read More: Linearization of smooth integrable systems

Anti-canonical bundle of singular foliations

Take a singular foliation say of dimension k.

Locally at each point there exists $k$ vector fields X1, …, Xk which are tangent to the foliation and which are linearly independent almost everywhere (we will only consider foliations which satisfy this property)

The wedge product L = X1…Xk is a Nambu structure tangent to . . . → Read More: Anti-canonical bundle of singular foliations

Linearization and stability of singular foliations

This is the topic that I want to talk about in the conference in honor of Alan Weinstein’s 70th birthday in EPFL (Lausanne) in July. This post is the place in keep the preparation for my talk.

A work of mine on the linearization of proper Lie groupoids was directly influenced by Alan (it . . . → Read More: Linearization and stability of singular foliations

A picture from GESTA 2013

Me giving the last lecture of my minicourse, Friday 07/June/2013, GESTA



The “tail of the cat”, which was drawn 3 times there on the blackboard,  was an example (of an exotic symplectic R^2n) that intrigued many people :D

Thanks to Truong Hong Minh for the picture, that he shot using his . . . → Read More: A picture from GESTA 2013

Oracle phổ quát bậc 2 ?

Ok, đây là tôi tự bổ túc văn hóa về complexity thôi.

Trong lý thuyết complexity, người ta nói đến các oracle, tức là các “hộp đen” để tính các hàm (hay trả lời các câu hỏi) nào đó,  chỉ cần cho input (thuộc loại nào đó) vào đấy thì sẽ ra ngay output, . . . → Read More: Oracle phổ quát bậc 2 ?

Mathematical Biology Activity

An activity in mathematical biology “Multiscale Modeling”:

Dear colleagues,

we are very pleased to announce the ESMTB-EMS Spring School

“Multiscale modeling in the life sciences”, Lyon, May 27-31 2013


Courses will be given by distinguished specialists in the field of Mathematical Biology.

Pierre Degond (Université Paul Sabatier, Toulouse) Dirk Drasdo (INRIA Rocquencourt) Bard . . . → Read More: Mathematical Biology Activity

Free online articles on (integrable) nonholonomic systems

Got an ad from Regular and Chaotic Dynamics:

The following RCD articles on non-holonomic systems, contact mechanics and applications will be available on free access at http://ics.org.ru/journals/rcd  till March 1, 2013.

V.V. Kozlov, On Invariant Manifolds of Nonholonomic Systems http://ics.org.ru/eng?menu=mi_pubs&abstract=1985

A.V. Borisov, A.A. Kilin, I.S. Mamaev, How to Control Chaplygin’s Sphere Using Rotors http://ics.org.ru/eng?menu=mi_pubs&abstract=2011

. . . → Read More: Free online articles on (integrable) nonholonomic systems

Weinstein Conference 07/2013

An international conference to celebrate the 70th birthday of Alan Weinstein (one of the founders of  symplectic and Poisson geometry) will take place at EPFL (Lausanne)  from 22 to 26 July 2013. A-priori, I’ll be in Lausanne for 4 weeks in July, and will take part in this conference.


. . . → Read More: Weinstein Conference 07/2013

Annales de Toulouse Mathématiques online

Annales de Toulouse is the journal of our Institut de Mathématiques de Toulouse. It is one of the oldest mathematical journals in the world, and many famous people published in this journal in the past. For example, Lyapunov published his stability theory there.

Recently, the journal became somewhat obscure due to various technical problems. . . . → Read More: Annales de Toulouse Mathématiques online

3 ngày ở nước Tí Hon

Đây là phần đầu bản dịch tiếng Việt mới của cuốn sách toán học dành cho trẻ em rất nổi tiếng nhan đề “3 ngày ở nước Tí Hon”, nguyên bản tiếng Nga là “Три дня в Карликании” của tác giả Vladimir Levshin.

Sở dĩ sách được dịch lại, vì bản dịch cũ của . . . → Read More: 3 ngày ở nước Tí Hon

Introduction to dynamical systems (1)

These are the notes for an optional course on dynamical systems that I will give to 4th year mathematics students this semester.

The course is in French, but for convenience I will write the notes in English. (In order to become competitive, my French students will have to learn to use English anyway).

The . . . → Read More: Introduction to dynamical systems (1)