Bifurcations and global stability of families of gradients
Publications Mathématiques de l'IHÉS, Tome 70 (1989), pp. 103-168. 
@article{PMIHES_1989__70__103_0,
     author = {Dias Carneiro, M. J. and Palis, Jacob},
     title = {Bifurcations and global stability of families of gradients},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {103--168},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {70},
     year = {1989},
     mrnumber = {1067381},
     zbl = {0706.58042},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1989__70__103_0/}
}
TY  - JOUR
AU  - Dias Carneiro, M. J.
AU  - Palis, Jacob
TI  - Bifurcations and global stability of families of gradients
JO  - Publications Mathématiques de l'IHÉS
PY  - 1989
SP  - 103
EP  - 168
VL  - 70
PB  - Institut des Hautes Études Scientifiques
UR  - http://www.numdam.org/item/PMIHES_1989__70__103_0/
LA  - en
ID  - PMIHES_1989__70__103_0
ER  - 
%0 Journal Article
%A Dias Carneiro, M. J.
%A Palis, Jacob
%T Bifurcations and global stability of families of gradients
%J Publications Mathématiques de l'IHÉS
%D 1989
%P 103-168
%V 70
%I Institut des Hautes Études Scientifiques
%U http://www.numdam.org/item/PMIHES_1989__70__103_0/
%G en
%F PMIHES_1989__70__103_0
Dias Carneiro, M. J.; Palis, Jacob. Bifurcations and global stability of families of gradients. Publications Mathématiques de l'IHÉS, Tome 70 (1989), pp. 103-168. http://www.numdam.org/item/PMIHES_1989__70__103_0/

[1] V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko, Singularities of differentiable maps, vol. I, Birkhäuser, 1985. | MR

[2] T. Bröker, Differentiable germs and catastrophes, Cambridge University Press, 1975. | Zbl

[3] J. Guckenheimer, Bifurcations and catastrophes, Dynamical Systems, Acad. Press, 1973, 95-109. | MR | Zbl

[4] B. A. Khesin, Local bifurcations of gradient vector fields, Functional Analysis and Appl., 20, 3 (1986), 250-252. | MR | Zbl

[5] N. H. Kuiper, C1-equivalence of functions near isolated critical points, in Symp. on Infinite Dim. Topology, Ann. of Math. Studies, 69, Princeton University Press, 1972, 199-218. | MR | Zbl

[6] R. Labarca, Stability of parametrized families of vector fields, in Dynamical Systems and Bifurcation Theory, Pitman Research Notes in Math. Series, 160 (1987), 121-214. | MR | Zbl

[7] J. Martinet, Singularities of smooth functions and maps, Lecture Notes Series, 58, London Math. Society, 1982. | MR | Zbl

[8] J. Martinet, Déploiements versels des applications différentiables et classification des applications stables, in Lecture Notes in Math., 535, Springer-Verlag, 1975, 1-44. | MR | Zbl

[9] J. Mather, Finitely determined maps germs, Publ. Math. I.H.E.S., 35 (1968), 127-156. | Numdam | Zbl

[10] O. E. Lanford Iii, Bifurcation of periodic solutions into invariant tori : the work of Ruelle and Takens, in Nonlinear Problems in the Physical Sciences and Biology, Lecture Notes in Math., 322, Springer-Verlag, 1973, 159-192. | Zbl

[11] S. Newhouse, J. Palis and F. Takens, Stable families of diffeomorphisms, Publ. Math. I.H.E.S., 57 (1983), 5-71. | Numdam | MR | Zbl

[12] R. Palais, Local triviality of the restriction map for embeddings, Comm. Math. Helvet., 34 (1962), 305-312. | MR | Zbl

[13] R. Palais, Morse theory on Hilbert manifolds, Topology, 2 (1963), 299-340. | MR | Zbl

[14] J. Palis, On Morse-Smale dynamical systems, Topology, 8 (1969), 385-405. | MR | Zbl

[15] J. Palis and F. Takens, Stability of parametrized families of gradient vector fields, Annals of Math., 118 (1983), 383-421. | MR | Zbl

[16] J. Palis and S. Smale, Structural stability theorems, in Global Analysis Proceedings Symp. Pure Math., 14, A.M.S., 1970, 223-231. | MR | Zbl

[17] S. Sternberg, On the structure of local homeomorphisms of euclidean space II, Amer. Journal of Math., 80 (1958), 623-631. | MR | Zbl

[18] F. Takens, Moduli of stability for gradients, in Singularities and Dynamical Systems, Mathematics Studies, 103, North-Holland, 1985, 69-80. | MR | Zbl

[19] F. Takens, Singularities of gradient vector fields and moduli, in Singularities and Dynamical Systems, Mathematics Studies, 103, North-Holland, 1985, 81-88. | MR | Zbl

[20] F. Takens, Partially hyperbolic fixed points, Topology, 10 (1971), 133-147. | MR | Zbl

[21] R. Thom, Stabilité structurelle et morphogenèse, Benjamin, 1972. | MR | Zbl

[22] G. Vegter, Bifurcations of gradient vector fields, Ph. D. Thesis, Groningen, 1983.

[23] G. Vegter, Global stability of generic two-parameter families of gradients on three manifolds, in Dynamical Systems and Bifurcations, Lecture Notes in Math., 1125, Springer-Verlag, 1985, 107-129. | MR | Zbl

[24] G. Vegter, The Cp-preparation theorem, Cp-unfoldings and applications, Report ZW-8013, Groningen, 1981.