Forgive your enemies, but never, never forget their names.
by John F. Kennedy

Mendeleev table – new style

It looks so beautiful and mathematical – it even has non-trivial monodromy – so I just have to steal it from Wikipedia and put it here :D

Dynamical Systems (5): Ergodicity

These are  the notes that i’m trying to write up for the 5th lecture of my doctoral course “Basic principles of dynamical systems” in Toulouse. This lecture is about ergodicity.

I’m behind schedule in many things, so please be patient with me. The correct lecture notes will appear one day. I’m even planning to . . . → Read More: Dynamical Systems (5): Ergodicity

Integrability Workshop in Rouen 14-16/Nov/2012

I’ll attend an integrability workshop in Rouen from 14 to 16 November 2012:

http://math.univ-lyon1.fr/~salnikov/disco/

 

Home page Poster Program List of participants Registration Social program Practical information Contact us

The registration is now open. Attention: the registration deadline is the 19th of October. Priliminary list of lecturers: Alain Albouy (Paris) Eva Miranda (Barcelona) Elie . . . → Read More: Integrability Workshop in Rouen 14-16/Nov/2012

Tại sao vấn đề P vs NP khó vậy (2)

[Cưỡi ngựa xem hoa] [Bổ sung lần cuối: 10/Sep/2012]

Trong bài viết trước (Tại sao vấn đề P vs NP khó vậy) chưa hề nói đến các vũ khí đã dùng “để tấn công thành trì P|NP” . Bài này sẽ thử liệt kê dần các “vũ khí thông dụng” đã dung trong các . . . → Read More: Tại sao vấn đề P vs NP khó vậy (2)

Tại sao vấn đề P vs NP khó vậy ?

Đây chỉ là một bài cưỡi ngựa xem hoa thôi, vì sự hiểu biết của tôi về tin học chỉ ở mức “lớp 1”. Tuy nhiên, nghe người ta nói “vấn đề P vs NP” là vấn đề lý thuyết “quan trọng nhất của thời đại” nên cũng phải tìm hiểu nó xem sao, . . . → Read More: Tại sao vấn đề P vs NP khó vậy ?

Complexification of real dynamical systems

I know very little about complex (meaning over the field of complex numbers, and not in the sense of complexity) dynamical systems. But by chance I’m invited to give a talk in a seminar on complex dynamics in Paris this week, so I have to find a topic which is close to my work . . . → Read More: Complexification of real dynamical systems

Intrinsic convexity of almost-toric integrable Hamiltonian systems

This is a work in progress with Christophe Wacheux, a student of San.

Christophe went to see me in Toulouse to discuss about his thesis. After several discussions, I gave him 2 problems to work on. The first  is about semi-local classification of integrable Hamiltonian systems up to exact isomorphisms (i.e. diffeomorphisms which preserve . . . → Read More: Intrinsic convexity of almost-toric integrable Hamiltonian systems

A note on commuting foliations (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)

Littlewood’s conjecture (1930)

Just learned about the following conjecture of Littlewood (1930), which looks very simple and which is apparently still open:

Let be two arbitrary real numbers. Denote by . Then

This conjecture is related to ergodic theory of It is not difficult to show that the set of pairs of number which donot satisfy . . . → Read More: Littlewood’s conjecture (1930)

Orbital linearization of smooth completely integrable vector fields (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)

Decomposition of Dynamical Systems

arXiv:0903.4617

I’m interested in all kinds of decomposition of all kinds of systems.

I’m planning to write a paper on the decomposition of dynamical systems into fundamental states. This project is a bit vague. I want to make some ideas/results more precise and easier to apply before writing things up.

By a “dynamical system” . . . → Read More: Decomposition of Dynamical Systems

Action-angle variables on Dirac manifolds (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)

Geometry of nonsingular integrable systems on 3-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)