Number and Amplitude of Limit Cycles emerging from {\it Topologically Equivalent} Perturbed Centers

Abstract

We consider three examples of weekly perturbed centers which do not have {\it 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: $dH(x,y)+\epsilon (f(x,y)dy-g(x,y)dx)=0$, with $H(x,y)=1/2(x^2+y^2)$. This reduction allows us to find the Melnikov function, $M(h)={\int }_{H=h}fdy-gdx$, 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.

17 pages, 0 figures

References in corpus (1)

• Variational approach to a class of nonlinear oscillators with several limit cycles

Cited by in corpus (1)

• Approximating the Amplitude and Form of Limit Cycles in the Weakly Nonlinear Regime of Lienard Systems