Structural stability of non-singular smooth vector fields on the torus can be investigated using the theory developed by Poincaré and Arnaud Denjoy. Using the Poincaré recurrence map, the question is reduced to determining structural stability of diffeomorphisms of the circle. As a consequence of the Denjoy theorem, an orientation preserving "C"2 diffeomorphism "ƒ" of the circle is structurally stable if and only if its rotation number is rational, "ρ"("ƒ") = "p"/"q", and the periodic trajectories, which all have period "q", are non-degenerate: the Jacobian of "ƒ""q" at the periodic points is different from 1, see circle map.