ArticleOriginal scientific text

Title

Implicit Differential Equations From the Singularity Theory Viewpoint

Authors 1, 1

Affiliations

  1. Department of Pure Mathematics, The University of Liverpool, PO Box 147, Liverpool L69 3BX, England

Bibliography

  1. V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, Berlin, 1983.
  2. Th. Brocker and L. C. Lander, Differentiable Germs and Catastrophes, London Math. Soc. Lecture Note Ser. 17, Cambridge University Press, 1975.
  3. J. W. Bruce, A note on first order differential equations of degree greater than one and wavefront evolution, Bull. London Math. Soc. 16 (1984), 139-144.
  4. J. W. Bruce, A. A. du Plessis and C. T. C. Wall, Determinacy and unipotency, Invent. Math. 88 (1987), 521-554.
  5. J. W. Bruce and D. Fidal, On binary differential equations and umbilics, Proc. Roy. Soc. Edinburgh 111A (1989), 147-168.
  6. J. W. Bruce and F. Tari, On binary differential equations, Nonlinearity 8 (1995), 255-271.
  7. L. Dara, Singularités génériques des équations différentielles multiformes, Bol. Soc. Brasil. Math. 6 (1975) 95-128.
  8. G. Darboux, Leçons sur la théorie générale des surfaces, Vol. 4, Gauthier-Villars, Paris, 1896.
  9. A. A. Davydov, Normal forms of differential equations unresolved with respect to derivatives in a neighbourhood of a singular point, Functional Anal. Appl. 19 (1985), 1-10.
  10. C. Gutierrez and J. Sotomayor, Structurally stable configurations of lines of principal curvature, Astérisque (1982), 98-99.
  11. C. Gutierrez and J. Sotomayor, Lines of curvature and umbilical points on surfaces, 18 Colóquio Brasileiro de Matemática, Instituto de Matemática Pura e Aplicada, Brasil, 1991.
  12. A. D. Myshkis, Differential inequalities with locally bounded derivatives, Zap. Mekh.-Mat. F-ta Khar'kovskigo Mat. O-va 30 (1964), 152-163.
  13. J. M. West, Ph. D. Thesis, Liverpool University, 1995.
  14. H. Whitney, On singularities of mappings of Euclidean spaces I, Mappings from the plane to the plane, Ann. of Math. 62 (1955), 374-410.
Pages:
23-38
Main language of publication
English
Published
1996
Exact and natural sciences