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 del testo si danno condizióni sufficienti affinché l'origine. sia un centro globale.
@article{RLIN_1991_9_2_4_281_0, author = {Marco Sabatini}, title = {A sufficient condition for a polynomial centre to be global}, journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni}, volume = {2}, year = {1991}, pages = {281-285}, zbl = {0757.34025}, mrnumber = {1152634}, language = {en}, url = {http://dml.mathdoc.fr/item/RLIN_1991_9_2_4_281_0} }
Sabatini, Marco. A sufficient condition for a polynomial centre to be global. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 2 (1991) pp. 281-285. http://gdmltest.u-ga.fr/item/RLIN_1991_9_2_4_281_0/
[1] Solution of the Problem of Centre and Focus in One Case. Prikl. Mat. Meth., 17, 1953, 333-338. (in russian). | MR 55521 | Zbl 0053.06203
,[2] About Centers of Planar Cubic Systems. Analytic Theory. Preprint, Firenze1987. | MR 956022
,[3] Centers of Polynomial Systems in . Dip. Mat. Appl. «G. Sansone», 5, Firenze 1990.
,[4] Generic Properties of Polynomial Vector Fields at Infinity. Trans. Amer. Math. Soc., 143, 1969, 201-222. | MR 252788 | Zbl 0187.34401
,[5] Some Properties of Planar Polynomial Systems of Even Degree. Ann. Mat. Pura Appl., to appear. | MR 1174822 | Zbl 0757.34023
- ,[6] | MR 658490 | Zbl 0476.34002
, Ordinary Differential Equations. Birkhauser, Boston1982.[7] On the Conditions for a Center. Diff. Uravnenya, 1, 1965, 176-181 (in russian). | MR 192117
- ,[8] Conditions for a Center in the Presence of Third Degree Homogeneous Nonlinearities. Diff. Uravnenya, 1, 1965, 1482-1487 (in russian). | MR 190436 | Zbl 0166.34704
- ,[9] | MR 121520 | Zbl 0089.29502
- , Qualitative Theory of Differential Equations. Princeton University Press, Princeton, New Jersey 1960.[10] On the Accumulation of Limit Cycles. Proc. A.M.S., 99, 1987, 515-526. | MR 875391 | Zbl 0626.34022
,[11] The methods of invariants in the qualitative theory of differential equations. Ak. Nauk. Moldav. SSR, Kishinev, 1968 (in russian).
, - , Equazioni differenziali non lineari. Cremonese, Roma 1956.