Advertisement

Geometric aspects of the singular solutions of certain differential equations

Conference paper
  • 417 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 209)

Keywords

Singular Point Total Degree Singular Solution Real Zero Real Analytic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    J. Milnor, Singular points of complex hypersurfaces, Annals of Math. Studies Princeton University Press, Study 61, 1968.Google Scholar
  2. [2]
    _____ On the Betti numbers of real varieties, Proc. A.M.S. 15 (1964)Google Scholar
  3. [3]
    R. Thom, Sur l’homologie des varietes algebriques reelles, Differential and Combinatorial Topology, Princeton University Press 1965, 225–265.Google Scholar
  4. [4]
    E.L. Ince, Ordinary Differential Equations, Dover, New York, 1956.Google Scholar
  5. [5]
    B. van der Waerden, Einführung in die algebraische Geometrie, Springer, Berlin, 1939.Google Scholar
  6. [6a]
    R. Courant & D. Hilbert, Methods of Mathematical Physics, Vol.II (Partial Differential Equations). Interscience (Wiley and Sons), 1965.Google Scholar
  7. [6b]
    P.R. Garabedian, Partial Differential Equations, Wiley and Sons, Inc., third edition, 1967.Google Scholar
  8. [7]
    I. Kaplansky, An introduction to differential algebra, Herman, Paris, 1957.zbMATHGoogle Scholar
  9. [8]
    E.R. Kolchin, Singular solutions of algebraic differential equations and a lemma of Arnold Shapiro, Topology 3 (supplement 2) 1965, 309–318.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [9a]
    _____ Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations, Ann. of Math. 49, (1948), 1–42.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [9b]
    E.R. Kolchin, Existence theorems connected with the Picard-Vessiot theory of homogeneous linear ordinary differential equations, Bull. Amer. Math. Soc. 54, (1948), 927–932.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [10]
    J.F. Ritt, Differential equations from the algebraic standpoint, Amer. Math. Soc. Coll. Pub., Vol.14, New York, 1932.Google Scholar
  13. [11]
    _____ Differential Algebra, Amer. Math. Soc. Coll. Pub. vol.33, New York, 1950.Google Scholar
  14. [12]
    S. Lojasiewicz, Ensembles semi-analytiques, Institute des Hautes Etudes Scientifiques, Bures-Sur-Yvette, France, 1965.Google Scholar
  15. [13]
    _____ Triangulation of semi-analytic sets, Annali della Scuola Normale Superiore di Pisa, Serie III, Vol.XVIII, Fasc. IV (1964).Google Scholar
  16. [14]
    J. Siciak, Studia Math. Vol.35, (1970).Google Scholar
  17. [15]
    R. Thom, Sur les Equations Différentielles multiformes et leurs intégrales singulières. (Manuscript).Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

There are no affiliations available

Personalised recommendations