Implicit Differential Equations From the Singularity Theory Viewpoint

• Autorzy: J. W. Bruce , F. Tari
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 23-38

Daty

wydano

1996

Twórcy

autor

J. W. Bruce

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

autor

F. Tari

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

Bibliografia

• [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.