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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 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 . Our results may be viewed as a contribution to proving (or disproving) a conjecture of Chicone and Jacobs.
A. Raouf Chouikha. "Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems." Applicationes Mathematicae 32.3 (2005): 305-325. <http://eudml.org/doc/279718>.
@article{A2005, 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.}, author = {A. Raouf Chouikha}, journal = {Applicationes Mathematicae}, keywords = {conservative systems; Loud systems}, language = {eng}, number = {3}, pages = {305-325}, title = {Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems}, url = {http://eudml.org/doc/279718}, volume = {32}, year = {2005}, }
TY - JOUR AU - A. Raouf Chouikha TI - Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems JO - Applicationes Mathematicae PY - 2005 VL - 32 IS - 3 SP - 305 EP - 325 AB - 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. LA - eng KW - conservative systems; Loud systems UR - http://eudml.org/doc/279718 ER -