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
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
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
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
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
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
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 ?
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)
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
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
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)
I’m stumbling over the problem of inversion of a unbounded operator on a Hilbert space. My operator is a perturbation of a Casimir operator acting by double differentiation of a tensor space. It ooks like an elliptic operator, so the inverse is expected to be (at least) bounded, with a “very reasonabe” bound. But . . . → Read More: Inverse of a unbounded operator ?
Last updated 10/March/2012: This article is now finished. See
19/02/2012: We’re behind schedule now. Need to speed up !!!
This is the sketch of a research article in progress with a student of mine. I’m making the sketch of what we want to put in the article, and he takes care of writing . . . → Read More: Rn-actions on n-dimensional manifolds (article in preparation)