메뉴 건너뛰기




Volumn 357, Issue 1, 2005, Pages 267-285

Dupin indicatrices and families of curve congruences

Author keywords

[No Author keywords available]

Indexed keywords


EID: 12744281727     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-04-03497-X     Document Type: Article
Times cited : (19)

References (31)
  • 1
    • 84976161935 scopus 로고
    • On binary differential equations and umbilics
    • MR 90e:58141
    • J.W. Bruce and D. Fidal, On binary differential equations and umbilics, Proc. Royal Soc. Edinburgh, 111A (1989), 147-168. MR 90e:58141
    • (1989) Proc. Royal Soc. Edinburgh , vol.111 A , pp. 147-168
    • Bruce, J.W.1    Fidal, D.2
  • 2
    • 23044519726 scopus 로고    scopus 로고
    • Bifurcations of implicit differential equations
    • MR 2001f:34005
    • J.W. Bruce, G.J. Fletcher and F. Tari, Bifurcations of implicit differential equations, Proc. Royal Soc. Edinburgh, 130A (2000), 485-506. MR 2001f:34005
    • (2000) Proc. Royal Soc. Edinburgh , vol.130 A , pp. 485-506
    • Bruce, J.W.1    Fletcher, G.J.2    Tari, F.3
  • 3
    • 12744270759 scopus 로고    scopus 로고
    • Zero curves of families of curve congruences
    • to appear in the (T. Gaffney & M.A.S. Ruas, Editors), ICMC - USP - São Carlos, Brazil, 29 July - 02 August, 2002
    • th Workshop on Real and Complex Singularities (T. Gaffney & M.A.S. Ruas, Editors), ICMC - USP - São Carlos, Brazil, 29 July - 02 August, 2002.
    • th Workshop on Real and Complex Singularities
    • Bruce, J.W.1    Fletcher, G.J.2    Tari, F.3
  • 4
    • 0000902530 scopus 로고
    • On binary differential equations
    • MR 96d:58124
    • J.W. Bruce and F. Tari, On binary differential equations, Nonlinearity, 8 (1995), 255-271. MR 96d:58124
    • (1995) Nonlinearity , vol.8 , pp. 255-271
    • Bruce, J.W.1    Tari, F.2
  • 6
    • 0031537913 scopus 로고    scopus 로고
    • Generic 1-parameter families of binary differential equations of Morse type
    • MR 98h:58123
    • J.W. Bruce and F. Tari, Generic 1-parameter families of binary differential equations of Morse type, Discrete and Continuous Dynamical Systems, Vol. 3, No. 1 (1997), 79-90. MR 98h:58123
    • (1997) Discrete and Continuous Dynamical Systems , vol.3 , Issue.1 , pp. 79-90
    • Bruce, J.W.1    Tari, F.2
  • 7
    • 0002196437 scopus 로고    scopus 로고
    • On the multiplicity of binary differential equations
    • MR 2001e:34004
    • J.W. Bruce and F. Tari, On the multiplicity of binary differential equations, J. of Differential Equations, 148 (1998), 122-147. MR 2001e:34004
    • (1998) J. of Differential Equations , vol.148 , pp. 122-147
    • Bruce, J.W.1    Tari, F.2
  • 8
    • 0034179016 scopus 로고    scopus 로고
    • Duality and implicit differential equations
    • MR 2001a:34007
    • J.W. Bruce and F. Tari, Duality and implicit differential equations, Nonlinearity, Vol. 13, No. 3 (2000), 791-812. MR 2001a:34007
    • (2000) Nonlinearity , vol.13 , Issue.3 , pp. 791-812
    • Bruce, J.W.1    Tari, F.2
  • 10
    • 51249188876 scopus 로고
    • Singularites generiques des equations differentielles multiforms
    • MR 58:7720
    • L. Dara, Singularites generiques des equations differentielles multiforms, Bol. Soc. Bras. Mat., No. 6 (1975), 95-129. MR 58:7720
    • (1975) Bol. Soc. Bras. Mat. , Issue.6 , pp. 95-129
    • Dara, L.1
  • 11
    • 0002274572 scopus 로고
    • Normal forms of differential equations unresolved with respect to derivatives in a neighbourhood of its singular point
    • MR 87d:58116
    • A.A. Davydov, Normal forms of differential equations unresolved with respect to derivatives in a neighbourhood of its singular point, Funct. Anal. Appl., 19 (1985), 1-10. MR 87d:58116
    • (1985) Funct. Anal. Appl. , vol.19 , pp. 1-10
    • Davydov, A.A.1
  • 12
    • 0000718192 scopus 로고
    • Smooth normal forms of folded elementary singular points
    • MR 97a:58169
    • A.A. Davydov and L. Ortiz-Bobadilla, Smooth normal forms of folded elementary singular points, J. Dynam. Control Systems, 1, no. 4 (1995), 463-482. MR 97a:58169
    • (1995) J. Dynam. Control Systems , vol.1 , Issue.4 , pp. 463-482
    • Davydov, A.A.1    Ortiz-Bobadilla, L.2
  • 13
    • 0005704063 scopus 로고    scopus 로고
    • Smooth normal forms of folded resonance saddles and nodes and complete classification of generic linear second order PDE's on the plane
    • World Sci. Publishing, MR 99g:35009
    • A.A. Davydov and E. Rosales-González, Smooth normal forms of folded resonance saddles and nodes and complete classification of generic linear second order PDE's on the plane, International Conference on Differential Equations (Lisboa, 1995), 59-68, World Sci. Publishing, 1998. MR 99g:35009
    • (1998) International Conference on Differential Equations (Lisboa, 1995) , pp. 59-68
    • Davydov, A.A.1    Rosales-González, E.2
  • 17
    • 0034376237 scopus 로고    scopus 로고
    • Lines of principal curvature around umbilics and Whitney umbrellas
    • MR 2001i:58083
    • R. Garcia, C. Gutierrez, J. Sotomayor, Lines of principal curvature around umbilics and Whitney umbrellas, Tohoku Math. J., (2) 52 (2000), no. 2, 163-172. MR 2001i:58083
    • (2000) Tohoku Math. J., (2) , vol.52 , Issue.2 , pp. 163-172
    • Garcia, R.1    Gutierrez, C.2    Sotomayor, J.3
  • 21
    • 0001139914 scopus 로고    scopus 로고
    • Lines of curvature, umbilic points and Carathéodory conjecture
    • MR 2000b:53005
    • C. Gutierrez and J. Sotomayor, Lines of curvature, umbilic points and Carathéodory conjecture, Resenhas 3 (1998), no. 3, 291-322. MR 2000b:53005
    • (1998) Resenhas , vol.3 , Issue.3 , pp. 291-322
    • Gutierrez, C.1    Sotomayor, J.2
  • 22
    • 0038116312 scopus 로고    scopus 로고
    • Positive quadratic differential forms: Linearization, finite determinacy and versal unfolding
    • MR 98h:58021
    • C. Gutierrez and V. Guíñez, Positive quadratic differential forms: linearization, finite determinacy and versal unfolding, Ann. Fac. Sci. Toulouse Math., (6) 5 (1996), no. 4, 661-690. MR 98h:58021
    • (1996) Ann. Fac. Sci. Toulouse Math., (6) , vol.5 , Issue.4 , pp. 661-690
    • Gutierrez, C.1    Guíñez, V.2
  • 23
    • 84966199279 scopus 로고
    • Positive quadratic differential forms and foliations with singularities on surfaces
    • MR 89h:57021
    • V. Guíñez, Positive quadratic differential forms and foliations with singularities on surfaces Trans. Amer. Math. Soc., 309 (1988), 447-502. MR 89h:57021
    • (1988) Trans. Amer. Math. Soc. , vol.309 , pp. 447-502
    • Guíñez, V.1
  • 24
    • 0041802428 scopus 로고
    • Locally stable singularities for positive quadratic differential forms
    • MR 95d:58105
    • V. Guíñez, Locally stable singularities for positive quadratic differential forms, J. Differential Equations, 110 (1994), no. 1, 1-37. MR 95d:58105
    • (1994) J. Differential Equations , vol.110 , Issue.1 , pp. 1-37
    • Guíñez, V.1
  • 25
    • 0043229478 scopus 로고    scopus 로고
    • Rank two codimension 1 singularities of positive quadratic differential forms
    • MR 98f:58144
    • V. Guíñez, Rank two codimension 1 singularities of positive quadratic differential forms, Nonlinearity, 10 (1997), no. 3, 631-654. MR 98f:58144
    • (1997) Nonlinearity , vol.10 , Issue.3 , pp. 631-654
    • Guíñez, V.1
  • 27
    • 0009932214 scopus 로고
    • Classification of generic integral diagrams and first order ordinary differential equations
    • MR 95e:58026
    • A. Hayakawa, G. Ishikawa, S. Izumiya, K. Yamaguchi, Classification of generic integral diagrams and first order ordinary differential equations, Internat. J. Math., 5 (1994), no. 4, 447-489. MR 95e:58026
    • (1994) Internat. J. Math. , vol.5 , Issue.4 , pp. 447-489
    • Hayakawa, A.1    Ishikawa, G.2    Izumiya, S.3    Yamaguchi, K.4
  • 28
    • 0038455616 scopus 로고
    • Nonclassical equations of mixed type and their applications in gas dynamics
    • Birkhäuser Verlag, Basel, MR 93h:35137
    • A.G. Kuz'min, Nonclassical equations of mixed type and their applications in gas dynamics, International Series of Numerical Mathematics, 109, Birkhäuser Verlag, Basel, 1992. MR 93h:35137
    • (1992) International Series of Numerical Mathematics , vol.109
    • Kuz'Min, A.G.1
  • 29
    • 0000216699 scopus 로고
    • Structurally stable configurations of lines of principal curvature
    • Astérisque, 98-99, Soc. Math. France, Paris, MR 85h:58006
    • J. Sotomayor and C. Gutierrez, Structurally stable configurations of lines of principal curvature, Bifurcation, ergodic theory and applications (Dijon, 1981), 195-215, Astérisque, 98-99, Soc. Math. France, Paris, 1982. MR 85h:58006
    • (1982) Bifurcation, Ergodic Theory and Applications (Dijon, 1981) , pp. 195-215
    • Sotomayor, J.1    Gutierrez, C.2
  • 30
    • 51249189650 scopus 로고
    • Sur les equations differentielles multiform et leur integrales singulieres
    • R. Thorn, Sur les equations differentielles multiform et leur integrales singulieres, Bol. Soc. Bras. Mat., Vol. 3, No. 1 (1971), 1-11. MR 49:8053
    • (1971) Bol. Soc. Bras. Mat. , vol.3 , Issue.1
    • Thorn, R.1
  • 31
    • 0010995817 scopus 로고
    • Constrained equations; a study of implicit differential equations and their discontinuous solutions
    • LNM Springer-Verlag, MR 58:24311
    • F. Takens, Constrained equations; a study of implicit differential equations and their discontinuous solutions, in: Structural stability, the theory of catastrophes, and applications in the sciences. LNM 525, Springer-Verlag, 1976. MR 58:24311
    • (1976) Structural Stability, the Theory of Catastrophes, and Applications in the Sciences , vol.525
    • Takens, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.