# Implicit Differential Equations From the Singularity Theory Viewpoint

Banach Center Publications (1996)

- Volume: 33, Issue: 1, page 23-38
- ISSN: 0137-6934

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topBruce, J., and Tari, F.. "Implicit Differential Equations From the Singularity Theory Viewpoint." Banach Center Publications 33.1 (1996): 23-38. <http://eudml.org/doc/262584>.

@article{Bruce1996,

author = {Bruce, J., Tari, F.},

journal = {Banach Center Publications},

keywords = {implicit differential equations; singularities; binary differential equations},

language = {eng},

number = {1},

pages = {23-38},

title = {Implicit Differential Equations From the Singularity Theory Viewpoint},

url = {http://eudml.org/doc/262584},

volume = {33},

year = {1996},

}

TY - JOUR

AU - Bruce, J.

AU - Tari, F.

TI - Implicit Differential Equations From the Singularity Theory Viewpoint

JO - Banach Center Publications

PY - 1996

VL - 33

IS - 1

SP - 23

EP - 38

LA - eng

KW - implicit differential equations; singularities; binary differential equations

UR - http://eudml.org/doc/262584

ER -

## References

top- [1] V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, Berlin, 1983. Zbl0507.34003
- [2] Th. Brocker and L. C. Lander, Differentiable Germs and Catastrophes, London Math. Soc. Lecture Note Ser. 17, Cambridge University Press, 1975. Zbl0302.58006
- [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. Zbl0503.34003
- [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. Zbl0685.34004
- [6] J. W. Bruce and F. Tari, On binary differential equations, Nonlinearity 8 (1995), 255-271. Zbl0830.34021
- [7] L. Dara, Singularités génériques des équations différentielles multiformes, Bol. Soc. Brasil. Math. 6 (1975) 95-128. Zbl0405.34045
- [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. Zbl0521.53003
- [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. Zbl0068.37101

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