A sufficient condition for a polynomial centre to be global
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 2 (1991) no. 4, pp. 281-285.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

A sufficient condition is given in order that a centre of a polynomial planar autonomous system be a global centre.
Per il sistema autonomo differenziale \( (S) \) del testo si danno condizióni sufficienti affinché l'origine.\( O \) sia un centro globale.
@article{RLIN_1991_9_2_4_a1,
     author = {Sabatini, Marco},
     title = {A sufficient condition for a polynomial centre to be global},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {281--285},
     publisher = {mathdoc},
     volume = {Ser. 9, 2},
     number = {4},
     year = {1991},
     zbl = {0757.34025},
     mrnumber = {55521},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1991_9_2_4_a1/}
}
TY  - JOUR
AU  - Sabatini, Marco
TI  - A sufficient condition for a polynomial centre to be global
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
PY  - 1991
SP  - 281
EP  - 285
VL  - 2
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_1991_9_2_4_a1/
LA  - en
ID  - RLIN_1991_9_2_4_a1
ER  - 
%0 Journal Article
%A Sabatini, Marco
%T A sufficient condition for a polynomial centre to be global
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 1991
%P 281-285
%V 2
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_1991_9_2_4_a1/
%G en
%F RLIN_1991_9_2_4_a1
Sabatini, Marco. A sufficient condition for a polynomial centre to be global. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 2 (1991) no. 4, pp. 281-285. http://geodesic.mathdoc.fr/item/RLIN_1991_9_2_4_a1/

[1] A. F. Andreev, Solution of the Problem of Centre and Focus in One Case. Prikl. Mat. Meth., 17, 1953, 333-338. (in russian). | MR | Zbl

[2] R. Conti, About Centers of Planar Cubic Systems. Analytic Theory. Preprint, Firenze 1987. | MR

[3] R. Conti, Centers of Polynomial Systems in \( \mathbb{R}^{2} \). Dip. Mat. Appl. «G. Sansone», 5, Firenze 1990.

[4] E. A. Gonzales Velasco, Generic Properties of Polynomial Vector Fields at Infinity. Trans. Amer. Math. Soc., 143, 1969, 201-222. | MR | Zbl

[5] M. Galeotti - M. Villarini, Some Properties of Planar Polynomial Systems of Even Degree. Ann. Mat. Pura Appl., to appear. | DOI | MR | Zbl

[6] Ph. Hartman, Ordinary Differential Equations. Birkhauser, Boston 1982. | MR | Zbl

[7] V. A. Lunkevich - K. S. Sibirskh, On the Conditions for a Center. Diff. Uravnenya, 1, 1965, 176-181 (in russian). | MR

[8] V. A. Lunkevich - K. S. Sibirskii, Conditions for a Center in the Presence of Third Degree Homogeneous Nonlinearities. Diff. Uravnenya, 1, 1965, 1482-1487 (in russian). | MR | Zbl

[9] V. V. Nemitskh - V. V. Stepanov, Qualitative Theory of Differential Equations. Princeton University Press, Princeton, New Jersey 1960. | MR | Zbl

[10] L. M. Perko, On the Accumulation of Limit Cycles. Proc. A.M.S., 99, 1987, 515-526. | DOI | MR | Zbl

[11] K. S. Sibirskh, The methods of invariants in the qualitative theory of differential equations. Ak. Nauk. Moldav. SSR, Kishinev, 1968 (in russian).

[12] G. Sansone - R. Conti, Equazioni differenziali non lineari. Cremonese, Roma 1956. | MR | Zbl