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Singularities of vector fields

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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.

    Google Scholar 

  2. J. Dieudonné,Foundations of Modern Analysis, New York, Acad. Press, 1960.

    MATH  Google Scholar 

  3. R. E. Gomory, Trajectories tending to a critical point in 3-space,Ann. of Math.,61 (1955), 140–153.

    Article  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Google Scholar 

  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.

    Google Scholar 

  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.

    MATH  Google Scholar 

  12. V. V. Nemytskii andV. V. Stepanov,Qualitative theory of differential equations, Princeton, Princeton Univ. Press, 1960.

    MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  15. A. Seidenberg, A new decision method for elementary algebra,Ann. of Math.,60 (1954), 365–374.

    Article  Google Scholar 

  16. J. Sotomayor, Generic 1-parameter families of flows on 2-manifolds,Publ. math. I.H.E.S., no 43 (1973), 5–46.

  17. S. Sternberg, On the structure of local homeomorphisms of euclideann-space-II,Am. J. Math.,80 (1958), 623–631.

    Article  MATH  Google Scholar 

  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).

  19. R. Thom,Stabilité structurelle et morphogenèse, New York, Benjamin, 1972.

    Google Scholar 

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Authors and Affiliations

  1. Instituto de Matemática, Pura e Aplicada, Rua Luiz de Camoes 68, Rio de Janeiro, Brasil

    Floris Takens

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  1. Floris Takens
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Research supported by the Organization of American States (O.A.S.).

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Takens, F. Singularities of vector fields. Publications Mathématiques de L’Institut des Hautes Scientifiques 43, 47–100 (1974). https://doi.org/10.1007/BF02684366

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  • DOI: https://doi.org/10.1007/BF02684366

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