7,705 reputation
12755
bio website perso-math.univ-mlv.fr/users/…
location Paris, France
age 35
visits member for 5 years, 3 months
seen Jul 2 at 19:03

I am a teacher and researcher at Université Paris-Est Créteil.


Jun
29
comment Finite-space dynamical systems
Just to comment on the many interesting answers at once: it appears that this question has a kind of trivial feel at first (the dynamics converges to a cycle, how boring), but really sparkles when one has an additional structure on the state space: algebraic (finite fields), combinatorial (finite cellular automata) for example. Then the interaction between the additional structure and the dynamics seems to be very subtle.
Jun
12
answered Continuity of length and area
Jun
10
comment Differentiability of polytope shadow areas
In fact, the same idea appears when one tries to make a Riemannian metric out of a Finsler metric by using the John ellipsoid, which is something I came across a few years ago.
Jun
9
answered Differentiability of polytope shadow areas
Jun
4
comment Examples of Smooth, Compact and Non-rigid Manifolds that Bound a Finite, Non-zero Volume
@ManfredWeis: I took the liberty to precise the question: for abstract Riemannian manifolds, an isometric deformation is precisely changing nothing.
Jun
4
revised Examples of Smooth, Compact and Non-rigid Manifolds that Bound a Finite, Non-zero Volume
precised the question in accordance with the comments.
Jun
4
comment Examples of Smooth, Compact and Non-rigid Manifolds that Bound a Finite, Non-zero Volume
I don't understand what you mean by an isometric deformation; do you mean "submanifold of $\mathbb{R}^n$" when you say "manifold"? Given your title, do you further mean hypersurfaces?
Jun
1
revised Simultaneous approximation of arbitrary functions in Hölder space and in $L^2(\mu)$ by a smooth function and its derivative
edited body
May
27
comment Maximizing entropy under constraints
@VaughnClimenhaga: thanks for the clarification; in fact one of the nice point is that we are able to consider several constraints $\int \varphi_k \,d\mu=0$, which complicate things a bit as one needs more than the intermediate value theorem to get surjectivity. At the moment, it seems that the reference given by Anthony Quas is closest to what I asked, but the Barreira-Saussol thread will have to be mentioned.
May
27
comment Maximizing entropy under constraints
@BarbaraSchapira: note that I chose a context (shift with Hölder potentials) where the existence of Gibbs measures and coincidence with equilibrium states is not an issue (unless we mean different things by Gibbs measure, which might be the case). Note also that I am asking about a constrained case, i.e. we restrict to measure satisfying a certain equality $\int \varphi \,d\mu=0$; I do not see how this is addressed by the usual equilibrium states.
May
27
revised Simultaneous approximation of arbitrary functions in Hölder space and in $L^2(\mu)$ by a smooth function and its derivative
Made the title more accurate
May
27
answered Simultaneous approximation of arbitrary functions in Hölder space and in $L^2(\mu)$ by a smooth function and its derivative
May
26
comment Maximizing entropy under constraints
Thanks for your detailed answer; I must say that a quick look at the references you mention did not enable me to find what I looked for: I found interpretation in terms of multifractal spectra of such maximization problems, but not the description of how a maximizing (Gibbs) measure can be found. But you warned about the fact that these are implicit, so I guess I just need to take a more careful look.
May
25
comment Maximizing entropy under constraints
@AnthonyQuas: the pointer to Christian Wolf and Tamara Kucherenko is so good that it could be made an answer; it seems after a quick look that their work does contain this application of our work. Thanks!
May
25
revised Simultaneous approximation of arbitrary functions in Hölder space and in $L^2(\mu)$ by a smooth function and its derivative
Corrected my guess to a less obviously flase one.
May
25
comment Simultaneous approximation of arbitrary functions in Hölder space and in $L^2(\mu)$ by a smooth function and its derivative
@ChristianRemling: you are of course right. I will edit my guess.
May
25
asked Maximizing entropy under constraints
May
25
comment Simultaneous approximation of arbitrary functions in Hölder space and in $L^2(\mu)$ by a smooth function and its derivative
@ChristianRemling: sorry, the question had a mistake: the first convergence is about the derivative $\varphi_n'$.
May
25
revised Simultaneous approximation of arbitrary functions in Hölder space and in $L^2(\mu)$ by a smooth function and its derivative
Corrected $(*)$
May
25
asked Simultaneous approximation of arbitrary functions in Hölder space and in $L^2(\mu)$ by a smooth function and its derivative