Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems
Tom 32 / 2005
Applicationes Mathematicae 32 (2005), 305-325
MSC: 34C15, 34C23, 34C25, 34C37, 37G15.
DOI: 10.4064/am32-3-5
Streszczenie
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.
