A sufficient condition for a polynomial centre to be global

Marco Sabatini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 4, page 281-285
  • ISSN: 1120-6330

Abstract

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A sufficient condition is given in order that a centre of a polynomial planar autonomous system be a global centre.

How to cite

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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 2.4 (1991): 281-285. <http://eudml.org/doc/244279>.

@article{Sabatini1991,
abstract = {A sufficient condition is given in order that a centre of a polynomial planar autonomous system be a global centre.},
author = {Sabatini, Marco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Planar autonomous systems; Singular points; Centres; global centre; differential system in the plane; cycle; polynomial systems of odd degree},
language = {eng},
month = {12},
number = {4},
pages = {281-285},
publisher = {Accademia Nazionale dei Lincei},
title = {A sufficient condition for a polynomial centre to be global},
url = {http://eudml.org/doc/244279},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Sabatini, Marco
TI - A sufficient condition for a polynomial centre to be global
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/12//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 4
SP - 281
EP - 285
AB - A sufficient condition is given in order that a centre of a polynomial planar autonomous system be a global centre.
LA - eng
KW - Planar autonomous systems; Singular points; Centres; global centre; differential system in the plane; cycle; polynomial systems of odd degree
UR - http://eudml.org/doc/244279
ER -

References

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  1. ANDREEV, A. F., Solution of the Problem of Centre and Focus in One Case. Prikl. Mat. Meth., 17, 1953, 333-338. (in russian). Zbl0053.06203MR55521
  2. CONTI, R., About Centers of Planar Cubic Systems. Analytic Theory. Preprint, Firenze1987. MR956022
  3. CONTI, R., Centers of Polynomial Systems in R 2 . Dip. Mat. Appl. «G. Sansone», 5, Firenze1990. 
  4. GONZALES VELASCO, E. A., Generic Properties of Polynomial Vector Fields at Infinity. Trans. Amer. Math. Soc., 143, 1969, 201-222. Zbl0187.34401MR252788
  5. GALEOTTI, M. - VILLARINI, M., Some Properties of Planar Polynomial Systems of Even Degree. Ann. Mat. Pura Appl., to appear. Zbl0757.34023MR1174822DOI10.1007/BF01759643
  6. HARTMAN, PH., Ordinary Differential Equations. Birkhauser, Boston1982. Zbl0476.34002MR658490
  7. LUNKEVICH, V. A. - SIBIRSKH, K. S., On the Conditions for a Center. Diff. Uravnenya, 1, 1965, 176-181 (in russian). MR192117
  8. LUNKEVICH, V. A. - SIBIRSKII, K. S., Conditions for a Center in the Presence of Third Degree Homogeneous Nonlinearities. Diff. Uravnenya, 1, 1965, 1482-1487 (in russian). Zbl0166.34704MR190436
  9. NEMITSKH, V. V. - STEPANOV, V. V., Qualitative Theory of Differential Equations. Princeton University Press, Princeton, New Jersey 1960. Zbl0089.29502MR121520
  10. PERKO, L. M., On the Accumulation of Limit Cycles. Proc. A.M.S., 99, 1987, 515-526. Zbl0626.34022MR875391DOI10.2307/2046356
  11. SIBIRSKH, K. S., The methods of invariants in the qualitative theory of differential equations. Ak. Nauk. Moldav. SSR, Kishinev, 1968 (in russian). 
  12. SANSONE, G. - CONTI, R., Equazioni differenziali non lineari. Cremonese, Roma1956. Zbl0075.26803MR88607

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