Uniqueness of algebraic limit cycles for quadratic systems

Journal of Mathematical Analysis and Applications

Volumn 261, Issue 1, 2001, Pages 85-99

  Chavarriga, Javier ^a   Giacomini, Hector ^b   Llibre, Jaume ^c  

^a UNIVERSITY OF LLEIDA   (Spain)

^b UNIVERSITÉ DE TOURS   (France)

^c UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035457187     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2001.7476     Document Type: Article

References (16)

1. J. Chavarriga, A new example of a quartic algebraic limit cycle for quadratic systems, Differential Integral Equations, in press.
2. Chavarriga J., Llibre J. On the algebraic limit cycles of quadratic systems. Proceedings of the IV Catalan Days of Applied Mathematics, Tarragona, 1998. 1998;Univ. Rovira Virgili, Tarragona. p. 17-24.
3. Chavarriga J., Llibre J. Invariant algebraic curves and rational first integrals for planar polynomial vector fields. J. Differential Equations. 169:2001;1-16.
4. J. Chavarriga, J. Llibre, and J. Sorolla, Algebraic limit cycles of quadratic systems, preprint, 1999.
5. Darboux G. Mémoire sur les équations différentielles algébrique du premier ordre et du premier degré (Mélanges). Bull. Sci. Math. 2:1878;60-96.
6. Evdokimenco R. M. Construction of algebraic paths and the qualitative investigation in the large of the properties of integral curves of a system of differential equations. Differential Equations. 6:1970;1349-1358.
7. Evdokimenco R. M. Behavior of integral curves of a dynamic system. Differential Equations. 9:1974;1095-1103.
8. Evdokimenco R. M. Investigation in the large of a dynamic system with a given integral curve. Differential Equations. 15:1979;215-221.
9. Filiptsov V. F. Algebraic limit cycles. Differential Equations. 9:1973;983-986.
10. Fulton W. Algebraic Curves: An Introduction to Algebraic Geometry. 1969;Benjamin, New York.
11. Jouanolou J. P. Equations de Pfaff algébriques. Lectures Notes in Mathematics. 708:1979;Springer-Verlag, New York/Berlin.
12. j. Acta Math. Sinica. 8:1958;23-35.
13. Boqian Shen. A sufficient and necessary condition of the existence of quartic curve limit cycles and separatrix cycle in a certain quadratic system. Ann. Differential Equations. 7:1991;282-288.
14. Yablonskii A. I. Limit cycles of a certain differential equations. Differential Equations. 2:1966;335-344.
15. Yanqian Ye. Theory of Limit Cycles. Transl. Math. Monogr. 66:1986;Amer. Math. Soc. Providence.
16. Zhifen Zhang, Tongren Ding, Wenzao Huang, Zhenxi Dong. Qualitative Theory of Differential Equations. Transl. Math. Monogr. 101:1992;Amer. Math. Soc. Providence.