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Singularities of vector fields. (English) Zbl 0279.58009

MSC:
37C75 Stability theory for smooth dynamical systems
34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
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References:
[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
[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
[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
[15] A. Seidenberg, A new decision method for elementary algebra,Ann. of Math.,60 (1954), 365–374. · Zbl 0056.01804
[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
[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.
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