Monotonicity of the period function of the Li\'enard equation of second kind

TL;DR

This paper investigates the monotonicity of the period function in Lie9nard II type systems, extending previous results to systems with position-dependent mass and providing conditions for isochronicity.

Contribution

It generalizes Chicone's monotonicity result to planar Hamiltonian systems with position-dependent mass and offers criteria for potential isochronicity.

Findings

Extended monotonicity conditions for Lie9nard II systems

Provided sufficient conditions for isochronicity

Generalized previous theoretical results to broader class of systems

Abstract

This paper is concerned with the monotonicity of the period function for closed orbits of systems of the Li\'enard II type equation given by $\ddot{x} + f(x)\dot{x}^{2} + g(x) = 0$. We generalize Chicone's result regarding the monotonicity of the period function to planar Hamiltonian vector fields in the presence of a position dependent mass. Sufficient conditions are also given for the isochronicity of the potential in case of such a system.