On periodic orbits in a slow–fast system with normally elliptic slowmanifold

摘要

In this note,we consider the bifurcation of a singular homoclinic orbit to periodic ones in a 4-dimensional slow–fast system of ordinary differential equations, having a 2-dimensional normally elliptic slow manifold, originally studied by Fe?kan and Rothos. Assuming an extra degree of differentiability on the system, we can refine their perturbation scheme, in particular the choice of approximate solution, and obtain improved estimates.