Singularities of vector fields. (English) Zbl 0279.58009


37C75 Stability theory for smooth dynamical systems
34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
Full Text: DOI Numdam EuDML


[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.
[2] J. Dieudonné,Foundations of Modern Analysis, New York, Acad. Press, 1960.
[3] R. E. Gomory, Trajectories tending to a critical point in 3-space,Ann. of Math.,61 (1955), 140–153. · Zbl 0068.29703 · doi:10.2307/1969625
[4] D. Grobman, Homeomorphisms of systems of differential equations,Dokl. Akad. Nauk,128 (1965).
[5] P. Hartman, On the local linearization of differential equations,Proc. A.M.S.,14 (1963), 568–573. · Zbl 0115.29801 · doi:10.1090/S0002-9939-1963-0152718-3
[6] M. Hirsch, C. C. Pugh andM. Shub,Invariant manifolds (to appear).
[7] M. Hirsch andC. C. Pugh, Stable manifolds and hyperbolic sets, inProceedings 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 Cin R. Abraham andJ. Robbin,Transversal mappings and flows, New York, Benjamin, 1967. · Zbl 0173.11001
[9] H. I. Levine, Singularities of Differentiable Mappings, Notes of Lectures of R. Thom in Bonn (1960). Appearedin 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 (inSéminaire H. Cartan, 1962–1963), Paris (5e), 1964.
[11] R. Narasimhan,Analysis on Real and Complex manifolds, Amsterdam, North-Holland, 1968. · Zbl 0188.25803
[12] V. V. Nemytskii andV. V. Stepanov,Qualitative theory of differential equations, Princeton, Princeton Univ. Press, 1960. · Zbl 0089.29502
[13] M. M. Peixoto,Teoria Geometrica dos Equaçoes diferenciais, Rio de Janeiro, I.M.P.A., 1969.
[14] C. C. Pugh andM. Shub, Linearization of Normally Hyperbolic Diffeomorphisms and Flows,Inv. Math.,10 (1970), 187–198. · Zbl 0206.25802 · doi:10.1007/BF01403247
[15] A. Seidenberg, A new decision method for elementary algebra,Ann. of Math.,60 (1954), 365–374. · Zbl 0056.01804 · doi:10.2307/1969640
[16] J. Sotomayor, Generic 1-parameter families of flows on 2-manifolds,Publ. math. I.H.E.S., no 43 (1973), 5–46. · Zbl 0279.58008
[17] S. Sternberg, On the structure of local homeomorphisms of euclideann-space-II,Am. J. Math.,80 (1958), 623–631. · Zbl 0083.31406 · doi:10.2307/2372774
[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 0569.58003
[19] R. Thom,Stabilité structurelle et morphogenèse, New York, Benjamin, 1972.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.