Structural stability of planar homogeneous polynomial vector fields: Applications to critical points and to infinity

Journal of Differential Equations

Volumn 125, Issue 2, 1996, Pages 490-520

  Llibre, Jaume ^a   Pérez Del Río, Jesús S ^b   Rodríguez, José Angel ^b  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b UNIVERSITY OF OVIEDO   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030102663     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.0038     Document Type: Article

References (20)

1. [AP] A. A. ANDRONOV AND L. PONTRJAGIN, Systemes grossiers, Acad. Sci. URRS 14 (1937), 247-250.
2. 2, Ann. Mat. Pura Appl. 4 (1968), 35-70.
3. [AKL] J. C. ARTÉS, R. E. KOOIJ, AND J. LLIBRE, Structurally stable quadratic vector fields, preprint, 1994.
4. [BM] M. BRUNELLA AND M. MIARI, Topological equivalence of a plane vector field with its principal part defined through Newton polyhedra, J. Differential Equations 85 (1990), 338-336.
5. [CL] A. CIMA AND J. LLIBRE, Algebraic and topological classification of the homogeneous cubic vector fields in the plane, J. Math. Anal. Appl. 147 (1990), 420-448.
6. [C] C. COLEMAN, Equivalence of planar dynamical and differential systems, J. Differential Equations 1 (1965), 222-233.
7. [Co] C. B. COLLINS, Algebraic classification of homogeneous polynomial vector fields in the plane, University of Waterloo, 1993, preprint.
8. [D] T. DATE, Classification and analysis of two-dimensional real homogeneous quadratic differential equation systems, J. Differential Equations 32 (1979), 311-334.
9. [DS] F. DUMORTIER AND D. S. SHAFER, Restrictions on the equivalence homeomorphism in stability of polynomial vector fields, J. London Math. Soc. 41 (1990), 100-108.
10. [G] E. A. GONZÁLEZ, Generic properties of polynomial vector fields at infinity, Trans. Amer. Math. Soc. 143 (1969), 201-222.
11. [Gb] C. GODBILLON, "Dynamical Systems on Surfaces," Springer-Verlag, Berlin/ New York, 1983.
12. [JL1] X. JARQUE AND J. LLIBRE, Structural stability of planar Hamiltonian polynomial vectors fields, Proc. London Math. Soc. 68 (1994), 617-640.
13. [JL2] X. JARQUE AND J. LLIBRE, Global structural stability of planar Hamiltonian vector fields, "Hamiltonian Dynamical Systems," IMA Volumes in Math. and Its Appl., pp. 171-180, Springer-Verlag, Berlin/New York, 1994.
14. [KKN] J. KOTUS, M. KRYCH, AND Z. NITECKI, Global structural stability of flows on open surfaces, "Memoirs Amer. Math. Soc.," Vol. 261, Amer. Math. Soc.. Providence, RI, 1982.
15. [M] L. MARKUS, Quadratic differential equations and non-associative algebras, "Annals of Mathematics Studies," Vol. 45, pp. 185-213, Princeton Univ. Press, Princeton, NJ, 1960.
16. [P] M. M. PEIXOTO, Structural stability on two-dimensional manifolds, Topology 1 (1962), 101-120.
17. [S1] D. S. SHAFER, Structural stability and generic properties of planar polynomial vector fields, Rev. Mat. Hisp. Amer. 3 (1987), 337-355.
18. [S2] D. S. SHAFER, Structure and stability of gradient polynomial vector fields, J. London Math. Soc. 41 (1990), 109-121.
19. [Si] K. S. SIBIRSKY, "Introduction to the Algebraic Theory of Invariants of Differential Equations," Manchester Univ. Press, Manchester, 1988.
20. [So] J. SOTOMAYOR, "Curves definides per equaçóes diferenciais no plano," Institute de Matemática Pura e Aplicada, Río de Janeiro, 1979.