Bifurcation and stability of families of hyperbolic vector fields in dimension three

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 14, Issue 1, 1997, Pages 119-142

  Plaza, Sergio ^a   Vera, Jaime ^b  

^a UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

^b UNIVERSIDAD CATÓLICA DEL NORTE   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039505989     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(97)80151-5     Document Type: Article

References (14)

1. M. J. CARNEIRO and J. PALIS, Bifurcations and global stability of two-parameter families of gradient vector fields, Publications Math. I.H.E.S., Vol. 10, 1990, pp. 103-168.
2. R. LABARCA, Stability of parametrized families of vector fields, Pitman Research Notes in Mathematics Series, Vol. 160, 1987, pp. 121-213.
3. R. LABARCA and S. PLAZA, Global stability of vector fields, Erg. Theory and Dyn. Systems, Vol. 13. 1993, pp. 737-766.
4. I. MALTA and J. PALIS, Families of vector fields with finite modulus of stability, Lectures Notes in Math., Vol. 898, 1980, pp. 212-229.
5. S. NEWHOUSE, On simple arcs between structurally stable flows, Lectures Notes in Math., Vol. 468, 1975, pp. 209-233.
6. S. NEWHOUSE and J. PALIS, Cycles and bifurcations theory, Asterisque, Vol. 31, 1976, pp. 44-140.
7. S. NEWHOUSE, J. PALIS and F. TAKENS, Bifurcation and stability of families of diffeomorphisms, Publ. Math. I.H.E.S., Vol. 57, 1983, pp. 5-71.
8. J. PALIS and F. TAKENS, Stability of parametrized families of gradient vector fields, Ann. of Math., Vol. 118, 1983, pp. 383-421.
9. S. PLAZA, Global stability of saddle-node bifurcation of periodic orbit for vector fields, Annales de la Faculté de Sciences de Toulouse, Vol. III, no 3, 1994, pp. 411-448.
10. J. ROBIN, Structural stability theorem, Annals of Math., Vol. 94, 1971, pp. 447-493.
11. C. ROBINSON, Structurally stability for vector fields, Annals of Math., Vol. 99, 1974, pp. 154-175.
12. S. SMALE, Differentiable dynamical systems, Bull. A.M.S., Vol. 73, 1967, pp. 747-817.
13. F. TAKENS, Normal form for certain singularities of vector fields, Ann. Inst. Fourier, Vol. 23 (2), 1973, pp. 163-195.
14. J. VERA, Stability of quasi-transversal bifurcation of vector fields on 3-dimensional manifolds, Preprint, 1994.