Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems

Volume 32 / 2005

A. Raouf Chouikha Applicationes Mathematicae 32 (2005), 305-325 MSC: 34C15, 34C23, 34C25, 34C37, 37G15. DOI: 10.4064/am32-3-5

Abstract

We first examine conditions implying monotonicity of the period function for potential systems with a center at $0$ (in the whole period annulus). We also present a short comparative survey of the different criteria. We apply these results to quadratic Loud systems $(L_{D,F})$ for various values of the parameters $D$ and $F$. In the case of noncritical periods we propose an algorithm to test the monotonicity of the period function for $(L_{D,F})$. Our results may be viewed as a contribution to proving (or disproving) a conjecture of Chicone and Jacobs.

Authors

  • A. Raouf ChouikhaLAGA
    Université Paris 13
    93430 Villetaneuse, France
    e-mail

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