On Chouikha’s isochronicity criterion

Abstract

Recently A.R.Chouikha gave a new characterization of isochronicity of center at the origin for the equation x'' + g(x) = 0, where g is a real smooth function de_ned in some neighborhood of 0 ϵ R. We present some new development of the subject. The present text is a short account of my paper "On Chouikha's isochronicity criterion", arXiv:1201.6503, where the proofs can be found. We correct the formulation of some results from the above paper.