### Hiến pháp

There can be no real individual freedom in the presence of economic insecurity.
by Chester Bowles (1901 - 1986)

## A general approach to the problem of action-angle variables (new version)

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

## Reduction and integrability of stochastic dynamical systems

Just submitted a joint paper with my student today, “only” 4 months behind schedule:

Reduction and Integrability of stochastic dynamical systems (PDF file)

Abstract:

This paper is devoted to the study of qualitative geometrical properties of stochastic dynamical systems, namely their symmetries, reduction and integrability. In particular, we show that an SDS which is . . . → Read More: Reduction and integrability of stochastic dynamical systems

## A general approach to the problem of action-angle variables

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

## Book chapter on the geometry of integrable non-Hamiltonian systems

Just finished my chapter for a book on integrable systems. In case anyone is interested, here is the PDF file:

IntegrableBarcelona2014

## Stratified affine spaces

These are quick notes for a joint work with Ch. Wacheux

Here, by an affine manifold, we mean a paracompact manifold with a locally flat affine structure. If the manifold is of dimension n, then near each point we have a chart whose coordinate functions are affine functions, and any local affine function is . . . → Read More: Stratified affine spaces

## Three lectures on singular foliations

For those who might be interested: This PDF file contains the slides of my 3-hour minicourse on singular foliations, given in the Workshop “GAP XII: Geometric Mechanics”, Internatinal Mathematical Forum of Tsing Hua University, Sanya, 10-14/March/2014:

http://zung.zetamu.net/Maths/Talks/FoliationsSanya2014.pdf

The main topic of this minicourse is the correspondence Singular Foliations <–> Nambu structures, and how . . . → Read More: Three lectures on singular foliations

## Notes on random systems 3: Liouville theorem for RDS

Extension of Liouville’s theorem to the case of RDS

The case without first integrals:

X_1, …, X_p are p generators of RDS on a compact manifold M of dimension p, which commute with each other, and whose deterministic parts are linearly independent everwhere. Then M is a  p-dimensional torus T^p with a periodic coordinate . . . → Read More: Notes on random systems 3: Liouville theorem for RDS

## Notes on random systems 2

What is a random fixed point ?

A reference: Ochs – Oseledets: Examples of  RDS on a closed unit ball without random fixed points. (So the topological fixed point theorem is NOT valid for RDS)

Definition. A random fixed point of a RDS \Phi over noise space (\Omega, \theta) (theta is the dynamics in . . . → Read More: Notes on random systems 2

## Notes on random systems 1: RDS vs NDS

Edited: 25/02/2014

These series of notes are for a research project that I’m doing with a student of mine. Some of what I write here will look quite stupid, because I myself know little about random dynamical systems.

I’ll explain why we’re interested in these systems later. But first, here . . . → Read More: Notes on random systems 1: RDS vs NDS

## Monodromy can kill global convexity!

We just got a rather surprising result in our joint research project with Christophe Wacheux (currently post-doc at EPFL) about the intrinstic convexity of singular affine spaces.

The problem is to study the intrinsic local and global convexity of the affine structure of the base space of integrable Hamiltonian systems whose singularities are nondegenerate . . . → Read More: Monodromy can kill global convexity!

## Thuật toán của người mất trí nhớ

Có một bài toán “khá đơn giản” sau về vấn đề thuật toán, tôi biết chắc chắn là giải được (vì có định lý về vấn đề này), có điều tôi thử tự tìm lời giải mà loay hoay mãi chưa ra:

Có một người ở một làng bị mất trí và được cho . . . → Read More: Thuật toán của người mất trí nhớ

## Commuting Foliations

Our paper with Truong Hong Minh entitled “Commuting Foliations” has been accepted for publication in a special isue dedicated to Alain Chenciner in the journal  Regular and Chaotic Dynamics

The most imporant part of this paper is actually the exposition of the relationship between singular foliations and Nambu structures: how to go from a . . . → Read More: Commuting Foliations

## Geometry and Physics XII, Hainan (China), 10-14/03/2014

Next year I’ll come to Sanya, Hainan, China to attend “GAP XII”, an international conference on geometry and physics.

The organizers said they would have money to cover local expenses for a number of participants, so if anyone is interested in visiting Sanya, please contact them (or contact me if you don’t know them)

. . . → Read More: Geometry and Physics XII, Hainan (China), 10-14/03/2014