Duality and implicit differential equations

Nonlinearity

Volumn 13, Issue 3, 2000, Pages 791-811

  Bruce, J W ^a   Tari, F ^b  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034179016     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/13/3/315     Document Type: Article

References (29)

1. Arnold V I 1983 Geometrical Methods in the Theory of Ordinary Differential Equations (Berlin: Springer)
2. Banchoff T, Gaffney T and McCrory C 1982 Cusps of Gauss Mappings (Pitman Research Notes in Mathematics vol 55) (London: Pitman)
3. Bruce J W 1984 A note on first order differential equations of degree greater than one and wavefront evolution Bull. London Math. Soc. 16 139-44
4. Bruce J W and Fidal D 1989 On binary differential equations and umbilics Proc. R. Soc. Edin. A 111 147-68
5. Bruce J W and Giblin P J 1992 Curves and Singularities 2nd edn (Cambridge: Cambridge University Press)
6. Bruce J W, Giblin P J and Tari F 1995 Families of surfaces: height functions, Gauss maps and duals Real and Complex Singularities (Pitman Research Notes in Mathematics vol 333) ed W L Marar (London: Pitman) pp 148-78
7. Bruce J W and Tari F 1995 On binary differential equations Nonlinearity 8 255-71
8. Bruce J W and Tari F 1997 Generic 1-parameter families of binary differential equations of Morse type Discrete Contin. Dynam. Syst. 3 79-90
9. Bruce J W and Tari F 1998 On the multiplicity of implicit differential equations J. Differ. Equ. 148 122-47
10. Bruce J W, Fletcher G J and Tari F 2000 Bifurcations of binary differential equations Proc. R. Soc. Edin. A 130 to appear
11. Bruce J W and Tari F 2000 On families of symmetric matrices Preprint
12. Bruce J W and Tari F 1996 Extrema of principal curvature and symmetry Proc. R. Soc. Edin. 39 397-402
13. Bruce J W and Wilkinson T C 1991 Folding maps and focal sets Proc. Warwick Symp. on Singularities (Springer Lecture Notes in Mathematics vol 1462) (Berlin: Springer) pp 63-72
14. Cibrario M 1932 Sulla reduzione a forma delle equationi lineari alle derviale parziale di secondo ordine di tipo misto Accademia di Scienze e Lettere, Instituto Lombardo Redicconti 65 889-906
15. Davydov A A 1985 Normal forms of differential equations unresolved with respect to derivatives in a neighbourhood of its singular point Funct. Anal. Appl. 19 1-10
16. Davydov A A 1994 Qualitative Control Theory (Translations of Mathematical Monographs vol 142) (Providence, RI: American Mathematical Society)
17. Davydov A A and Ortiz-Bobadilla L 1995 Smooth normal forms of folded elementary singular points J. Dynam. Control Syst. 1 463-82
18. Eisenhart L P 1909 Differential Geometry (Ginn and Company)
19. Fletcher G J 1996 Geometrical problems in computer vision PhD Thesis Liverpool University
20. Guinez V 1988 Positive quadratic differential forms and foliations with singularities on surfaces Trans. Am. Math. Soc. 309 447-502
21. Koenderink J 1990 Solid Shape (Cambridge, MA: MIT press)
22. Kuz' min A G 1992 Nonclassical Equations of Mixed Type and their Applications in Gas Dynamics (International Series of Numerical Mathematics vol 109) (Basel: Birkhäuser)
23. Landis E 1981 Tangential singularities Funct. Anal. Appl. 15 103-14
24. Morris R J 1991 Symmetry of curves and the geometry of surfaces: two explorations with the aid of computer graphics Thesis University of Liverpool
25. Platonova O 1981 Singularities of mutual position of surface and a line Russ. Math. Surv. 36 248-9
26. Shcherbak O P 1982 Projectively dual space curves and Legendre singularities Trudy Tbliss. Univ. 232-3 Shcherbak O P 1982 Trudy Tbliss. Univ. 280-336 (Engl. transl. 1986 Selecta Math. Sov. 5 391-421)
27. Shcherbak O P 1982 Projectively dual space curves and Legendre singularities Trudy Tbliss. Univ. 232-3 Shcherbak O P 1982 Trudy Tbliss. Univ. 280-336 (Engl. transl. 1986 Selecta Math. Sov. 5 391-421)
28. Shcherbak O P 1982 Projectively dual space curves and Legendre singularities Trudy Tbliss. Univ. 232-3 Shcherbak O P 1982 Trudy Tbliss. Univ. 280-336 (Engl. transl. 1986 Selecta Math. Sov. 5 391-421)
29. Wilkinson TC 1991 The geometry of folding maps Thesis University of Newcastle-upon-Tyne