Geodesic
Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems
A. Raouf Chouikha1
1 LAGA Université Paris 13 93430 Villetaneuse, France
Applicationes Mathematicae, Tome 32 (2005) no. 3, pp. 305-325 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/am32-3-5
Keywords: first examine conditions implying monotonicity period function potential systems center whole period annulus present short comparative survey different criteria apply these results quadratic loud systems various values parameters noncritical periods propose algorithm test monotonicity period function results may viewed contribution proving disproving conjecture chicone jacobs

A. Raouf Chouikha 1

1 LAGA Université Paris 13 93430 Villetaneuse, France 
@article{10_4064_am32_3_5,
     author = {A. Raouf Chouikha},
     title = {Monotonicity of the period function for
 some planar differential systems.
 {Part} {I:} {Conservative} and quadratic systems},
     journal = {Applicationes Mathematicae},
     pages = {305--325},
     year = {2005},
     volume = {32},
     number = {3},
     doi = {10.4064/am32-3-5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am32-3-5/}
}
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
SP  - 305
EP  - 325
VL  - 32
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am32-3-5/
DO  - 10.4064/am32-3-5
LA  - en
ID  - 10_4064_am32_3_5
ER  - 
%0 Journal Article
%A A. Raouf Chouikha
%T Monotonicity of the period function for
 some planar differential systems.
 Part I: Conservative and quadratic systems
%J Applicationes Mathematicae
%D 2005
%P 305-325
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/am32-3-5/
%R 10.4064/am32-3-5
%G en
%F 10_4064_am32_3_5
A. Raouf Chouikha. Monotonicity of the period function for
 some planar differential systems.
 Part I: Conservative and quadratic systems. Applicationes Mathematicae, Tome 32 (2005) no. 3, pp. 305-325. doi: 10.4064/am32-3-5

Cité par Sources :