# Loïc Teyssier

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bio website www-irma.u-strasbg.fr/… location Strasbourg age 36 member for 1 year, 10 months seen 4 hours ago profile views 856
I'm working on complex dynamical systems, more specifically on the local/global aspect of singular holomorphic foliations in the complex plane

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 Apr16 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 $\ddot y$. Apr16 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. Apr16 comment An elementary question in abstract algebra Please, do not answer non-research level questions… Apr16 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. Apr16 comment How to find a matrix by its characteristic value and characteristic vectors? Please, do not answer questions which are not research level… Apr14 awarded Revival Apr14 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 ;) Apr14 comment Non-hyperbolic fixed points in multidimensional systems @Nathaniel: see my edit. Apr14 revised Non-hyperbolic fixed points in multidimensional systems added 567 characters in body Apr14 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 Apr14 revised The centralizer of Lienard equation added 20 characters in body Apr14 answered Non-hyperbolic fixed points in multidimensional systems Apr13 answered The centralizer of Lienard equation Apr11 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. Apr11 revised Integer roots of a polynomial According to the comments, j can be any integer Apr11 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. Apr11 comment Integer roots of a polynomial @HAMEDHM: edit done Apr11 suggested suggested edit on Integer roots of a polynomial Apr11 comment Integer roots of a polynomial @HAMEDHM: wait, do you mean that $j$ can be negative ? Apr11 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…?