On the geometry in the neighborhood of infinity of quadratic differential systems with a weak focus

Qualitative Theory of Dynamical Systems

Volumn 2, Issue 1, 2001, Pages 1-43

  Schlomiuk, Dana ^a   Pal, Janos ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b Systems MGMT Department Level 3   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84896693138     PISSN: 15755460     EISSN: 16623592     Source Type: Journal    
DOI: 10.1007/BF02969379     Document Type: Article

References (19)

1. A.A. Andronov, E.A. Leontovich, J.J. Gordon and A.G. Maier, Qualitative theory of second-order systems, Wiley, New York, 1973.
2. N.N. Bautin, On the number of limit cycles which appear with the variations of coefficients from an equilibrium position of focus or center type, Transl. Amer. Math. Soc. Ser. 100(1) (1954), 397-413.
3. M. Brunella and M. Miari, Topological equivalence of a planar vector field with its principal part defined through Newton Polyhedra, Journal of Differential Equation, 85 (1990), 338-366.
4. C. Camacho, Complex foliations arising from Polynomial Differential Equations, Notes by Maria Izabel Camacho, in Bifurcations and Periodic Orbits of Vector Fields, (Edited by D. Schlomiuk), 1-19, Kluwer Academic Publishers, (1993).
5. W. Fulton, Algebraic curves, W.A. Benjamin, Inc., 226 pages, (1969).
6. W. Fulton Introduction to intersection theory in Algebraic Geometry, A.M.S. -conference Board of the Math. Sciences, Regional Conference Series in Math. Number 54.
7. I. Nikolaev and N. Vulpe, Topological classification of quadratic systems at infinity, J. London Math. Soc. (2)55(1997), 473-488.
8. J. Pal and D. Schlomiuk, Summing up the dynamics of the quadratic hamiltonian systems with a center, Canad. J. Math. 49(3)(1997), 583-599.
9. J. Pal and D. Schlomiuk, On the geometry at infinity of quadratic systems with a weak focus, Preprint, September, 1999, 46 pages.
10. J. Pal and D. Schlomiuk, Intersection multiplicity and limit cycles in quadratic systems with a weak focus, Preprint September 1999, 34 pages.
11. H. Poincaré, Mémoire sur les courbes définies par leséquations différentielles, J. de Math. Pures Appl. 1(4)(1985), 167-244.
12. J.W. Reyn and R.E. Kooij, Infinite singular points of quadratic systems in the plane, Nonlinear Analysis, Theory, Methods and Applications 24 (1995), 895-927.
13. D. Schlomiuk, Basic algebro-geometric concepts in the study of planar polynomial vector fields, Publicacions Matemátiques 41(1997), 269-295.
14. Shi Songling, A method of constructing cycles withtout contact around a weak focus, J. Diff. Equations 41(1981), 301-312.
15. Shi Songling, On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields, J. Diff. Equations 52 (1984), 52-57.
16. K.S. Sibirsky, Introduction to the algebraic theory of invariants of differential equations, Manchester Universsity Press, (1988), 169 pages. (Original Russian Edition 1982.)
17. N.I. Vulpe, Affine-invariant conditions for the topological discrimination of quadratic systems with a center, Translated from Differentsial'nye Uravneniya, 19, No. 3, 371-379, (1983).
18. Qin Yuanxun, Shi Songling and Cai Suilin, On limit cycles of planar Quadratic System, Scientia Sinica (Series A), Vol. 25 No 1, January 1982, 41-50.
19. Ye Yanqian, et al., The theory of limit cycles, Trans. Math. Monographs, Vol. 66 A.M.S., (1986).