Limit cycles bifurcating from a two-dimensional isochronous cylinder

The goal of this work is to illustrate the explicit implementation of a method for computing limit cycles which bifurcate from a continuum of isochronous periodic orbits forming a subset of Rn of dimension k < n when we perturb it inside a class of C2 differential systems. The method is based on the averaging theory. As far as we know, up to the present all the applications of this method for n > 2 have been performed by perturbing a linear center which fills a whole Rk ⊂ Rn. Here we will perturb the cylinder x2 + y2 = 1 of R3 = {(x, y, z) : x, y, z ∈ R} filled with periodic orbits. © 2009 Elsevier Ltd. All rights reserved.