Geodesic
Quadratic systems with limit cycles of normal size
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2003), pp. 31-46

Voir la notice de l'article provenant de la source Math-Net.Ru

In the class of planar autonomous quadratic polynomial differential systems we provide 6 different phase portraits having exactly 3 limit cycles surrounding a focus, 5 of them have a unique focus. we also provide 2 different phase portraits having exactly 3 limit cycles surrounding one focus and 1 limit cycle surrounding another focus. the existence of the exact given number of limit cycles is proved using the dulac function. all limit cycles of the given systems can be detected through numerical methods; i.e. the limit cycles have “a normal size” using perko's terminology. 
@article{BASM_2003_1_a3,
     author = {Leonid A. Cherkas and Joan C. Art\'es and Jaume Llibre},
     title = {Quadratic  systems with limit cycles of normal size},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {31--46},
     publisher = {mathdoc},
     number = {1},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2003_1_a3/}
}
TY  - JOUR
AU  - Leonid A. Cherkas
AU  - Joan C. Artés
AU  - Jaume Llibre
TI  - Quadratic  systems with limit cycles of normal size
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2003
SP  - 31
EP  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2003_1_a3/
LA  - en
ID  - BASM_2003_1_a3
ER  - 
%0 Journal Article
%A Leonid A. Cherkas
%A Joan C. Artés
%A Jaume Llibre
%T Quadratic  systems with limit cycles of normal size
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2003
%P 31-46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2003_1_a3/
%G en
%F BASM_2003_1_a3
Leonid A. Cherkas; Joan C. Artés; Jaume Llibre. Quadratic  systems with limit cycles of normal size. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2003), pp. 31-46. http://geodesic.mathdoc.fr/item/BASM_2003_1_a3/