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Questions related from Gabriel Thomas
Let a trajectory of a real dynamical system be : X(t)=\Phi(x_0, t_0, t). We suppose that a subsequence ( X_n = \Phi(x_0, t_0, t_n) ) where t_n= t_0+ \lambda n is a linear sequence of instants,...
05 November 2020 3,470 8 View
Consider a 2-dimensional ODE in the real plane. An equivalence relation is defined among the points a, b in the plane : aRb if an only if there is a trajectory connecting a and b. The space of...
21 February 2019 2,750 0 View
I am looking for differential equations (polynomial) such that : - there is a singular solution. - the differential ideal is prime. I guess it does not actually exist : we know that for a given...
23 August 2018 9,418 6 View
Hello, Supposing that the stars S1 and S2 orbit around their barycenter and S1 is two or three times much heavier than S2. Say the average distance between these stars is about 100 Mkm so that...
18 April 2018 7,730 4 View
Given a conical curve in the euclidean plane, I am looking for references on parameterizations using rational functions. It means : x=x(t) and y=y(t), assuming that x(t) and y(t) are rational...
27 December 2017 4,424 4 View
Dear all, I am working on the diff. system dy/dx=(1+y^3)/3, with the initial condition y(0)=0. By formal integration I obtain that y-->\+infty when x-->\alpha with \alpha=\sqrt(3)\pi/2 i.e....
29 October 2016 5,176 5 View
Dear all, I have, for an example, the following differential equation : y' = 1- y^3 The formal integration yields -ln(abs(y-1))+1/2 ln(1+y+y^2)+sqrt(3)Arctan((2y+1)/sqrt(3)) - y_0 = z - z_0 Any...
14 April 2016 4,001 5 View
Consider an ODE X'=F(X) where F is a polynomial in the Xi, with coefficients in Q or an algebraic extension of Q. n>=2 is the dimension of the space of X. Then the period T of any periodic...
07 November 2015 1,095 0 View
