Linearizations, normalizations and isochrones of planar differential systems

In the first section we collect some unpublished results presented in [17], related to linearizations and normalizations of planar centers. In the second section we consider both the problem of finding isochrones of isochronous systems (centers or not) and its inverse, i.e. given a family of curves filling an open set, how to construct a system having such curves as isochrones. In particular, we show that for every family of curves y = mx+d(x), m ∈ IR, there exists a Liénard system having such curves as isochrones