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1617
bio website www-irma.u-strasbg.fr/…
location Strasbourg
age 36
visits member for 1 year, 10 months
seen 4 hours ago
I'm working on complex dynamical systems, more specifically on the local/global aspect of singular holomorphic foliations in the complex plane

Apr
16
comment The centralizer of Lienard equation
@AliTaghavi: the trick you mentionned with the vector field obtained by looking for an autonomous sytem satisfied by $\dot \gamma$, seems to work only in that specific case (or other «simple» cases). Otherwise you can't get rid of the variables $x, y$ in the expression of $\ddot x=\dot y\frac{\partial P}{\partial x}(x,y)+\dot y\frac{\partial P}{\partial y}(x,y)$ and the same for $\ddot y$.
Apr
16
comment The centralizer of Lienard equation
@AliTaghavi: no, it's not true. Take the linear center case $P(x,y)=y, Q(x,y)=-x$. Then $X\cdot P=Q$ and $X\cdot Q=-P$ so that you obtain a multiple of the radial vector field.
Apr
16
comment An elementary question in abstract algebra
Please, do not answer non-research level questions…
Apr
16
comment How to find a matrix by its characteristic value and characteristic vectors?
Welcome to MO. This site is for reseach level questions. You should try to ask this question on another site, like MathStackExchange.
Apr
16
comment How to find a matrix by its characteristic value and characteristic vectors?
Please, do not answer questions which are not research level…
Apr
14
awarded  Revival
Apr
14
comment The centralizer of Lienard equation
@AliTaghavi: well, I may be wrong! But the heuristics is as follows: transverse commuting vector fields give Lie symmetries and improve integrability (by quadrature on the underlying differential equation $\frac{dy}{dx}=\ldots$). But it seems to me that the system is not integrable (in that sense) when $F$ is "too complicated". Yet I'm no specialist of Liénard systems, I'd rather trust you on that subject ;)
Apr
14
comment Non-hyperbolic fixed points in multidimensional systems
@Nathaniel: see my edit.
Apr
14
revised Non-hyperbolic fixed points in multidimensional systems
added 567 characters in body
Apr
14
comment “Explicit” examples of Irrational numbers very well approximated by rationnal numbers
@few_reps: I don't talk to bosses as a general rule ;) Bises
Apr
14
revised The centralizer of Lienard equation
added 20 characters in body
Apr
14
answered Non-hyperbolic fixed points in multidimensional systems
Apr
13
answered The centralizer of Lienard equation
Apr
11
comment Limit cycles as closed geodesics(geodesiable flow)
@AliTaghavi: I'm afraid I can't tell for sure that I followed your argument. Anyway, I hope your interesting question will find an aswer.
Apr
11
revised Integer roots of a polynomial
According to the comments, j can be any integer
Apr
11
comment Is there a program for convenient working with equations and coefficients?
You need to use a symbolic calculator (computer algebra system). Try Maple, PARI and the like (some are free and others not). Yet this question is not fit for this site and will surely be closed soon, so you might want to ask the question elsewhere.
Apr
11
comment Integer roots of a polynomial
@HAMEDHM: edit done
Apr
11
suggested suggested edit on Integer roots of a polynomial
Apr
11
comment Integer roots of a polynomial
@HAMEDHM: wait, do you mean that $j$ can be negative ?
Apr
11
comment Limit cycles as closed geodesics(geodesiable flow)
@AliTaghavi: although your approach is interesting in that case, I don't understand how you hope to relate it to Hilbert 16th's problem when there is more than 1 limit cycle…?