Monotonicity of the period function of the Liénard equation of second kind

2016/08/08 by A Ghose-Choudhury, Ghose-Choudhury, A, Partha Guha +1
Mathematics · Physics and Astronomy · #34C14 #34C20 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:34C14 #msc:34C20

paper · pdf · doi:10.48550/arxiv.1608.02910

submitted to journal

arxiv created 2016/08/08 · arxiv updated 2016/08/10

Abstract

This paper is concerned with the monotonicity of the period function for closed orbits of systems of the Liénard II type equation given by x + f(x)x² + 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.

Related

• The Period Function of Second Order Differential Equations
• Monotonicity of the period function for planar Hamiltonian vector fields: A Generalization of Chicone's Criterion
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• Periodic Perturbations of Non-Conservative Second Order Differential Equations
• Monotonicity and critical points of the period function for potential system