# Loïc Teyssier

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bio website www-irma.u-strasbg.fr/… location Strasbourg age 36 member for 1 year, 9 months seen 3 hours ago profile views 784
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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 Jan14 comment Curve on two-sphere generating an open set? Seconding Sasha's comment, your question admits a positive answer with Peano-like curves. Jan10 comment System of 2 linear q-difference equations with singular matrix @user2983638: how do you compute the numerical solutions? Jan10 comment System of 2 linear q-difference equations with singular matrix In general you begin by looking at formal power series solutions, then study convergence. What you typically obtain are q-sumable series, admitting a q-Gevrey asymptotic expansion near $x=0$, guaranteeing continuity of "genuine" solutions. If you don't have this property then the problem is an order of magnitude more difficult... Jan10 comment System of 2 linear q-difference equations with singular matrix ... But you'll have to wander in the complex line to understand things like Stokes phenomena, even if you start from real functions. Jan10 comment System of 2 linear q-difference equations with singular matrix There is some litterrature about q-Gevrey resumation of divergent formal power series solution to q-difference equations, which seems to be your case. This study is relatively recent, check papers by Ramis, Sauloy, Zhang etc. Jan10 comment System of 2 linear q-difference equations with singular matrix Maybe the "matrix" $\prod_{i=0}^\infty A^{-1}(q^i x)$ is not a matrix... (does the infinite product converges?). Without specifics about the $a_{ij}$ the question seems difficult to answer. In particular it is not clear to me why $\det A(0)=0$ and $\det (I-A(0))\neq 0$ should hold. Dec19 comment Recurrence formula for digamma function with rational number I guess you had a look at the wikipedia page en.wikipedia.org/wiki/Digamma_function#Gaussian_sum. There are some nice formulas, but maybe not quite what you're looking for. Dec14 comment Characterization of Differentiability via Lie Derivatives Sorry I misread your statement. My apologizes. Dec14 comment Characterization of Differentiability via Lie Derivatives I guess that you use $k$ for different purposes in your statement. Dec13 awarded Popular Question Dec12 comment Does there exist a linear equation system with a NAND-like behavior? If all variables are real and all (in)equations are linear then the set described by the system is convex. Then surely the condition $x_3=0\Rightarrow x_1=x_2=1$ is impossible since the solution set will contain the whole segment $[(0,0,0) , (1,1,0) ]$. Dec12 comment Does there exist a linear equation system with a NAND-like behavior? This question does not seem research level to me (see the FAQ). Besides, without context it's hard to guess why we should be bothered to solve this exercise or disprove the statement (no offense meant). Dec11 revised The holomorphic version of Galois theory deleted 2 characters in body Dec11 comment The holomorphic version of Galois theory I'm no specialist, but Riemann manifolds of algebraic functions are compact for the Zariski topology, and thus compact as projective manifolds by Chow's theorem. I hope I'm not too much mistaken saying things in that way (again, I'm no specialist of these questions). The reference I found is a paper by Zariski himself : "The compactness of the Riemann manifold of an abstract field of algebraic functions." (1944) with MR number MR0011573. I hope this covers your (essential) objection. Dec11 comment The holomorphic version of Galois theory @AliTaghavi: See edited answer. I removed all my comments since they were incorporated in the edit. Dec11 revised The holomorphic version of Galois theory added 14 characters in body Dec11 answered The holomorphic version of Galois theory Dec8 revised Homeomorphism of the circle with rational rotation number added 55 characters in body Nov17 comment How do I solve this nonlinear ODE with a fractional order term Your $L$ also depends on $x_0$ (try $x_0:=0$). Nov14 revised Non-linear first order ODE Changed 'y' by 'f' as in the OP