Abstract

We consider planar differential equations of the form $z˜=f(z)g(ar\; z)$ being $f(z)$ and $g(z)$ holomorphic functions and prove that if $g(z)$ is not constant then for any continuum of period orbits the period function has at most one isolated critical period, which is a minimum. Among other implications, the paper extends a well known result for meromorphic equations, $z˜=h(z)$, that says that any continuum of periodic orbits has a constant period function

This is a joint work with A. Garijo and X. Jarque.