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 R n of dimension k < n when we perturb it inside a class of C 2 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 R k ⊂ R n . Here we will perturb the cylinder x 2 + y 2 = 1 of R 3 = { ( x , y , z ) : x , y , z ∈ R } filled with periodic orbits.