Singularities of vector fields
Publications Mathématiques de l'IHÉS, Volume 43 (1974), p. 47-100
@article{PMIHES_1974__43__47_0,
author = {Takens, Floris},
title = {Singularities of vector fields},
journal = {Publications Math\'ematiques de l'IH\'ES},
publisher = {Institut des Hautes \'Etudes Scientifiques},
volume = {43},
year = {1974},
pages = {47-100},
zbl = {0279.58009},
mrnumber = {49 \#4052},
language = {en},
url = {http://www.numdam.org/item/PMIHES_1974__43__47_0}
}

Takens, Floris. Singularities of vector fields. Publications Mathématiques de l'IHÉS, Volume 43 (1974) pp. 47-100. http://www.numdam.org/item/PMIHES_1974__43__47_0/

[1] H. F. De Baggis, Dynamical systems with stable structures, in S. LEFSCHETZ, Contributions to the theory of nonlinear oscillations II, Princeton, Princeton Univ. Press, 1952. | MR 14,557a | Zbl 0047.33002

[2] J. Dieudonné, Foundations of Modern Analysis, New York, Acad. Press, 1960. | MR 22 #11074 | Zbl 0100.04201

[3] R. E. Gomory, Trajectories tending to a critical point in 3-space, Ann. of Math., 61 (1955), 140-153. | MR 16,700b | Zbl 0068.29703

[4] D. Grobman, Homeomorphisms of systems of differential equations, Dokl. Akad. Nauk, 128 (1965). | MR 22 #12282 | Zbl 0100.29804

[5] P. Hartman, On the local linearization of differential equations, Proc. A.M.S., 14 (1963), 568-573. | MR 27 #2693 | Zbl 0115.29801

[6] M. Hirsch, C. C. Pugh and M. Shub, Invariant manifolds (to appear). | Zbl 0355.58009

[7] M. Hirsch and C. C. Pugh, Stable manifolds and hyperbolic sets, in Proceedings of the A.M.S. Summer Institute on Global Analysis, Berkeley, Univ. Press, 1967.

[8] A. Kelley, The stable, center-stable, center, center-unstable and unstable manifolds. Published as appendix C in R. ABRAHAM and J. ROBBIN, Transversal mappings and flows, New York, Benjamin, 1967. | MR 36 #4096 | Zbl 0173.11001

[9] H. I. Levine, Singularities of Differentiable Mappings, Notes of Lectures of R. Thom in Bonn (1960). Appeared in Proceedings of Liverpool Singularities, Symposium I, Lecture Notes in Math., 192, Berlin, Springer Verlag, 1971.

[10] B. Malgrange, Le théorème de préparation en géométrie différentiable (in Séminaire H. Cartan, 1962-1963), Paris (5e), 1964. | Numdam | Zbl 0119.28501

[11] R. Narasimhan, Analysis on Real and Complex manifolds, Amsterdam, North-Holland, 1968. | MR 40 #4972 | Zbl 0188.25803

[12] V. V. Nemytskii and V. V. Stepanov, Qualitative theory of differential equations, Princeton, Princeton Univ. Press, 1960. | MR 22 #12258 | Zbl 0089.29502

[13] M. M. Peixoto, Teoria Geometrica dos Equaçoes diferenciais, Rio de Janeiro, I.M.P.A., 1969.

[14] C. C. Pugh and M. Shub, Linearization of Normally Hyperbolic Diffeomorphisms and Flows, Inv. Math., 10 (1970), 187-198. | MR 44 #1055 | Zbl 0206.25802

[15] A. Seidenberg, A new decision method for elementary algebra, Ann. of Math., 60 (1954), 365-374. | MR 16,209a | Zbl 0056.01804

[16] J. Sotomayor, Generic 1-parameter families of flows on 2-manifolds, Publ. math. I.H.E.S., n° 43 (1973), 5-46. | Numdam | Zbl 0279.58008

[17] S. Sternberg, On the structure of local homeomorphisms of euclidean n-space-II, Am. J. Math., 80 (1958), 623-631. | MR 20 #3336 | Zbl 0083.31406

[18] F. Takens, A non-stabilizable jet of a singularity of a vector field, to appear in the Proceedings of the Symposium on Dynamical Systems in Salvador (1971). | Zbl 0283.58009

[19] R. Thom, Stabilité structurelle et morphogenèse, New York, Benjamin, 1972. | MR 58 #7722a | Zbl 0294.92001