Number and amplitude of limit cycles emerging from topologically equivalent perturbed centers
نویسنده
چکیده
We consider three examples of weekly perturbed centers which do not have geometrical equivalence: a linear center, a degenerate center and a non-hamiltonian center. In each case the number and amplitude of the limit cycles emerging from the period annulus are calculated following the same strategy: we reduce of all of them to locally equivalent perturbed integrable systems of the form: dH(x, y) + ǫ(f(x, y)dy− g(x, y)dx) = 0, with H(x, y) = 1 2 (x + y). This reduction allows us to find the Melnikov function, M(h) = ∫ H=h fdy − gdx, associated to each particular problem. We obtain the information on the bifurcation curves of the limit cycles by solving explicitly the equation M(h) = 0 in each case.
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