Bifurcation and stability of families of hyperbolic vector fields in dimension three
Plaza, Sergio ; Vera, Jaime
Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997), p. 119-142 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1997-01-01
@article{AIHPC_1997__14_1_119_0,
     author = {Plaza, Sergio and Vera, Jaime},
     title = {Bifurcation and stability of families of hyperbolic vector fields in dimension three},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {14},
     year = {1997},
     pages = {119-142},
     mrnumber = {1437191},
     zbl = {0879.58056},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1997__14_1_119_0}
}

Plaza, Sergio; Vera, Jaime. Bifurcation and stability of families of hyperbolic vector fields in dimension three. Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) pp. 119-142. http://gdmltest.u-ga.fr/item/AIHPC_1997__14_1_119_0/

[C-P] 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. | Numdam | Zbl 0706.58042

[La] R. Labarca, Stability of parametrized families of vector fields, Pitman Research Notes in Mathematics Series, Vol. 160, 1987, pp. 121-213. | MR 907893 | Zbl 0632.58026

[La-Pl] R. Labarca and S. Plaza, Global stability of vector fields, Erg. Theory and Dyn. Systems, Vol. 13, 1993, pp. 737-766. | MR 1257032 | Zbl 0798.58044

[Ma-P] I. Malta and J. Palis, Families of vector fields with finite modulus of stability, Lectures Notes in Math., Vol. 898, 1980, pp. 212-229. | MR 654891 | Zbl 0482.58023

[N] S. Newhouse, On simple arcs between structurally stable flows, Lectures Notes in Math., Vol. 468, 1975, pp. 209-233. | MR 650638 | Zbl 0307.58011

[N-P] S. Newhouse and J. Palis, Cycles and bifurcations theory, Asterisque, Vol. 31, 1976, pp. 44-140. | MR 516408 | Zbl 0322.58009

[N-P-T] 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. | Numdam | MR 699057 | Zbl 0518.58031

[P-T] J. Palis and F. Takens, Stability of parametrized families of gradient vector fields, Ann. of Math., Vol. 118, 1983, pp. 383-421. | MR 727698 | Zbl 0533.58018

[Pl] S. Plaza, Global stability of saddle-node bifurcation of periodic orbit for vector fields, Annales de la Faculté de Sciences de Toulouse, Vol. III, n° 3, 1994, pp. 411-448. | Numdam | MR 1313357 | Zbl 0831.58036

[Ro] J. Robin, Structural stability theorem, Annals of Math., Vol. 94, 1971, pp. 447-493. | MR 287580 | Zbl 0224.58005

[Rob] C. Robinson, Structurally stability for vector fields, Annals of Math., Vol. 99, 1974, pp. 154-175. | MR 334283 | Zbl 0275.58012

[Sm] S. Smale, Differentiable dynamical systems, Bull. A.M.S., Vol. 73, 1967, pp. 747- 817. | MR 228014 | Zbl 0202.55202

[Ta] F. Takens, Normal form for certain singularities of vector fields, Ann. Inst. Fourier, Vol. 23 (2), 1973, pp. 163-195. | Numdam | MR 365620 | Zbl 0266.34046

[Ve] J. Vera, Stability of quasi-transversal bifurcation of vector fields on 3-dimensional manifolds, Preprint, 1994.