Period function and characterizations of Isochronous potentials

Abstract

We are interested at first in the study of the monotonicity for the period function of the conservative equation \ $(1)\ddot{x}+g(x)=0.$\quad Some refinements of known criteria are brought. Moreover, we give necessary and sufficient conditions so that the analytic potential of equation $(1)$ is isochronous. These conditions which are different from those introduced firstly by Koukles and Piskounov and thereafter by Urabe appear sometime to be easier to use. We then apply these results to produce families of isochronous potentials depending on many parameters, some of them are news. Moreover, analytic isochronicity requirements of parametrized potentials will also be considered

30 pages

References in corpus (2)

• A remark on rational isochronous potentials
• On the quantum spectrum of isochronous potentials

Cited by in corpus (3)

• On the Isochronous analytic motions and the quantum spectrum
• On the monotonicity criteria of the period function of potential systems
• Monotonicity of the period function of the Liénard equation of second kind