Quantities at infinity in translational polynomial vector fields

Bulletin des Sciences Mathematiques

Volumn 130, Issue 4, 2006, Pages 360-375

  Liu, Yirong ^a   Wang, Qinlong ^a,b  

^a CENTRAL SOUTH UNIVERSITY   (China)

^b YANGTZE UNIVERSITY   (China)

Author keywords

Bifurcation of limit cycles; Quantities at infinity; Translational polynomial system

Indexed keywords

EID: 33646893915     PISSN: 00074497     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.bulsci.2006.02.003     Document Type: Article

References (14)

1. Ye Y. Qualitative Theory of Polynomial Differential Systems (1995), Shanghai Sci. Tech. Publ., Shanghai (in Chinese)
2. Li J. Hilbert's 16th problem and bifurcations of planar polynomial vector fields. International Journal of Bifurcation and Chaos 33 (2003) 47-106
3. Blows T.R., and Rousseau C. Bifurcation at infinity in polynomial vector fields. Journal of Differential Equations 104 (1993) 215-242
4. Han M. Stability of the Equator and Bifurcation of Limit Cycles (1993), World Scientific
5. Liu Y., and Li J. Theory of values of singular point in complex autonomous differential system. Science in China (Series A) 33 (1990) 10-24
6. Liu Y. Theory of center-focus for a class of higher-degree critical points and infinite points. Science in China (Series A) 44 (2001) 37-48
7. Liu Y., and Chen H. Stability and bifurcations of limit cycles of the equator in a class of cubic polynomial systems. Computers and Mathematics with Applications 44 (2002) 997-1005
8. Huang W., and Liu Y. Bifurcations of limit cycles from infinity for a class of quintic polynomial system. Bulletin des Sciences Mathematiques 128 (2004) 291-302
9. Huang W., and Liu Y. A polynomial differential system with nine limit cycles at infinity. Computers and Mathematics with Applications 48 (2004) 577-588
10. Huang W., and Liu Y. A cubic polynomial system with six limit cycles at infinity. Journal of Central South University (Science and Technology) 35 (2004) 690-693
11. Zolsdek H. Eleven small limit cycles in a cubic vector field. Nonlinearity 8 (1995) 843-860
12. Lloyd N.G., and Pearson J.M. Symmetry in planar dynamical systems. Journal of Symbolic Computation 33 (2002) 357-366
13. 2-equivariant vector fields. Chaos, Solitons and Fractals 24 (2005) 329-348
14. Liu Y., and Huang W. A cubic system with twelve small amplitude limit cycles. Bulletin des Sciences Mathematiques 129 (2005) 83-98