The period function and the harmonic balance method

TL;DR

This paper investigates the properties of period functions in non-isochronous systems and demonstrates that the harmonic balance method can effectively analyze these properties, providing insights into local and global behavior.

Contribution

It establishes a connection between the properties of period functions and the harmonic balance method, showing the latter's effectiveness in studying non-isochronous systems.

Findings

Properties of period functions near critical points and infinity

Global monotonicity of period functions

Harmonic Balance Method replicates these properties

Abstract

In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or infinity, or their global monotonicity. Secondly, we show that these properties are also present when we approach to the same questions using the Harmonic Balance Method.