메뉴 건너뛰기




Volumn 13, Issue 1, 2005, Pages 139-162

Two-parameter families of implicit differential equations

Author keywords

Bifurcations; Implicit differential equations; Singularities

Indexed keywords


EID: 18144380314     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2005.13.139     Document Type: Article
Times cited : (16)

References (28)
  • 2
    • 18144393626 scopus 로고
    • Dynamical systems. V. Bifurcation theory and catastrophe theory
    • Springer-Verlag, Berlin
    • V.I. Arnold (Ed.), Dynamical systems. V. Bifurcation theory and catastrophe theory. Encyclopaedia of Mathematical Sciences, 5. Springer-Verlag, Berlin, 1994.
    • (1994) Encyclopaedia of Mathematical Sciences , vol.5
    • Arnold, V.I.1
  • 3
    • 0003348254 scopus 로고
    • Cusps of Gauss Mappings
    • Pitman (Advanced Publishing Program), Boston, Mass.-London
    • T. Banchoff, T. Gaffney and C. McCrory, Cusps of Gauss Mappings. Research Notes in Mathematics, 55. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982.
    • (1982) Research Notes in Mathematics , vol.55
    • Banchoff, T.1    Gaffney, T.2    McCrory, C.3
  • 4
    • 0001998334 scopus 로고
    • A note on differential equations of degree greater than one and wavefront evolution
    • J.W. Bruce, A note on differential equations of degree greater than one and wavefront evolution. Bull. London Math. Soc. 16 (1984), 139-144.
    • (1984) Bull. London Math. Soc. , vol.16 , pp. 139-144
    • Bruce, J.W.1
  • 7
    • 0002196437 scopus 로고    scopus 로고
    • On the multiplicity of implicit differential equations
    • J.W. Bruce and F. Tari, On the multiplicity of implicit differential equations. J. Differential Equations 148 (1998), 122-147.
    • (1998) J. Differential Equations , vol.148 , pp. 122-147
    • Bruce, J.W.1    Tari, F.2
  • 8
    • 12744281727 scopus 로고    scopus 로고
    • Dupin indicatrices and families of curve congruences
    • J.W. Bruce and F. Tari, Dupin indicatrices and families of curve congruences. Trans. Amer. Math. Soc. 357 (2005), 267-285.
    • (2005) Trans. Amer. Math. Soc. , vol.357 , pp. 267-285
    • Bruce, J.W.1    Tari, F.2
  • 10
    • 0001527087 scopus 로고
    • Sulla reduzione a forma delle equationi lineari alle derviate parziale di secondo ordine di tipo misto
    • M. Cibrario, Sulla reduzione a forma delle equationi lineari alle derviate parziale di secondo ordine di tipo misto. Accademia di Scienze e Lettere, Instituto Lombardo Redicconti 65 (1932), 889-906.
    • (1932) Accademia Di Scienze E Lettere, Instituto Lombardo Redicconti , vol.65 , pp. 889-906
    • Cibrario, M.1
  • 11
    • 51249188876 scopus 로고
    • Singularité génériques des équations differentielles multiformes
    • L. Dara, Singularité génériques des équations differentielles multiformes. Bol. Soc. Brasil. Math. 6 (1975), no. 2, 95-128.
    • (1975) Bol. Soc. Brasil. Math. , vol.6 , Issue.2 , pp. 95-128
    • Dara, L.1
  • 12
    • 0002274572 scopus 로고
    • Normal forms of differential equations unresolved with respect to derivatives in a neighbourhood of its singular point
    • A.A. Davydov, Normal forms of differential equations unresolved with respect to derivatives in a neighbourhood of its singular point. Functional Anal. Appl. 19 (1985), 1-10.
    • (1985) Functional Anal. Appl. , vol.19 , pp. 1-10
    • Davydov, A.A.1
  • 14
    • 0000718192 scopus 로고
    • Smooth normal forms of folded elementary singular points
    • A.A. Davydov and L. Ortiz-Bobadilla, Smooth normal forms of folded elementary singular points. J. Dynam. Control Systems 1 (1995), no. 4, 463-482.
    • (1995) J. Dynam. Control Systems , vol.1 , Issue.4 , pp. 463-482
    • Davydov, A.A.1    Ortiz-Bobadilla, L.2
  • 16
    • 0002336002 scopus 로고
    • Techniques in the theory of local bifurcations: Blow-up, normal forms, nilpotent bifurcations, singular perturbations. Bifurcations and periodic orbits of vector fields (Montreal, PQ, 1992)
    • Kluwer Acad. Publ., Dordrecht
    • F. Dumortier, Techniques in the theory of local bifurcations: blow-up, normal forms, nilpotent bifurcations, singular perturbations. Bifurcations and periodic orbits of vector fields (Montreal, PQ, 1992), 19-73, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 408, Kluwer Acad. Publ., Dordrecht, 1993.
    • (1993) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , vol.408 , pp. 19-73
    • Dumortier, F.1
  • 20
    • 0041802428 scopus 로고
    • Locally stable singularities for positive quadratic differential forms
    • V. Guíñez, Locally stable singularities for positive quadratic differential forms. J. Differential Equations, 110 (1994), 1-37.
    • (1994) J. Differential Equations , vol.110 , pp. 1-37
    • Guíñez, V.1
  • 21
    • 0009932214 scopus 로고
    • Classification of generic integral diagrams and first order ordinary differential equations
    • 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.
    • (1994) Internat. J. Math. , vol.5 , Issue.4 , pp. 447-489
    • Hayakawa, A.1    Ishikawa, G.2    Izumiya, S.3    Yamaguchi, K.4
  • 22
    • 0038455616 scopus 로고
    • Nonclassical equations of mixed type and their applications in gas dynamics
    • Birkhauser Verlag, Basel
    • A.G. Kuz'min, Nonclassical equations of mixed type and their applications in gas dynamics. International Series of Numerical Mathematics, 109. Birkhauser Verlag, Basel, 1992.
    • (1992) International Series of Numerical Mathematics , vol.109
    • Kuz'min, A.G.1
  • 24
    • 84983729155 scopus 로고    scopus 로고
    • On pairs of regular foliations in the plane
    • R.D.S. Oliveira and F. Tari, On pairs of regular foliations in the plane. Hokkaido Math. J. 31 (2002), no. 3, 523-537.
    • (2002) Hokkaido Math. J. , vol.31 , Issue.3 , pp. 523-537
    • Oliveira, R.D.S.1    Tari, F.2
  • 26
    • 0000216699 scopus 로고
    • Structurally stable configurations of lines of principal curvature. Bifurcation, ergodic theory and applications (Dijon, 1981)
    • Soc. Math. France, Paris
    • 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.
    • (1982) Astérisque , vol.98-99 , pp. 195-215
    • Sotomayor, J.1    Gutierrez, C.2
  • 27
    • 51249189650 scopus 로고
    • Sur les équations différentielles multiforms et leur intégrales singulières
    • R. Thom, Sur les équations différentielles multiforms et leur intégrales singulières. Bol. Soc. Brasil. Mat. 3 (1971), no. 1, 1-11.
    • (1971) Bol. Soc. Brasil. Mat. , vol.3 , Issue.1 , pp. 1-11
    • Thom, R.1
  • 28
    • 0000521365 scopus 로고
    • Finite determinacy of smooth mappings
    • C.T.C. Wall, Finite determinacy of smooth mappings. Bull. London Math. Soc. 13 (1981), 481-539.
    • (1981) Bull. London Math. Soc. , vol.13 , pp. 481-539
    • Wall, C.T.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.