Author(s)

Raouf Chouikha

Abstract

Comparison of Monotonicity Conditions for Periodic Functions Raouf Chouikha 1. Introduction: We are interested on a Newtonian Hamiltonian system 7~L(x. y) = (l/2)y -\- ^), started at the origine. This equation can be written where G is a %)rimitive of g'. The origin is surrounded by a continious family of periodic orbits. Each orbit lies on an energy level, 7Y(z. ?/) = c. and it is uniquely determined by c. The period function T(c) is the minimal period of this orbit. Many authors gave conditions on G and its derivatives for the period of the orbit to be monotone or to have critical points. Some of them give sufficient conditions for the period function to be monotonic. including Chicone [2], Chow and Wang [3], Rot he [4] and Shaaf [5]. Accordingly, we consider the following technical hypothesis

Keywords