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Consider the torus [tex]T^2[/tex] as a subset of R^3, for example the inverse image of 0 by the function [tex]f(x,y,z)=(\sqrt{x^2+y^2}-1)^2+z^2-4[/tex].

I need to obtain a example of a vector field [tex]X[/tex] defined in the whole [tex]R^3[/tex], such that:

1) [tex]X[/tex] is invariant in the torus

2) the orbits of [tex]X[/tex] in the torus are all periodic of the same period (I thought in something like the orbits being the parallels).

I can obtain such a v.f. in cylindrical coordinates, but when I put my example in cartesian coords, the equations are turning to be very complicated to my purpose, may be someone has a simpler example of such v.f.?

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# Differential equation in the torus

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