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Volumn 35, Issue 7, 1988, Pages 863-880

Normal Forms for Nonlinear Vector Fields— Part I: Theory and Algorithm

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES -- VECTORS;

EID: 0024037022     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/31.1833     Document Type: Article
Times cited : (70)

References (18)
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    • (1983)
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  • 4
    • 51649178043 scopus 로고
    • Singularities of vector fields
    • F. Takens, “Singularities of vector fields,” Publ. Math. I.H.E.S., vol. 43, pp. 47-100, 1974.
    • (1974) Publ. Math. I.H.E.S. , vol.43 , pp. 47-100
    • Takens, F.1
  • 5
    • 0002948647 scopus 로고
    • Normal forms for singularities of vector fields
    • S. Ushiki, “Normal forms for singularities of vector fields,” Japan J. Appl. Math., vol. 1, pp. 1-37, 1984.
    • (1984) Japan J. Appl. Math. , vol.1 , pp. 1-37
    • Ushiki, S.1
  • 8
    • 0000144083 scopus 로고
    • Normal forms for certain singularities of vector fields
    • F. Takens, “Normal forms for certain singularities of vector fields,” Ann. Inst. Fourier, vol. 23, pp. 163-195, 1973.
    • (1973) Ann. Inst. Fourier , vol.23 , pp. 163-195
    • Takens, F.1
  • 9
    • 0002533366 scopus 로고
    • Forced oscillations and bifurcations
    • Rijkuniversitet, Utrecht
    • ——_, “Forced oscillations and bifurcations,” Comm. Math. Inst., Rijkuniversitet, Utrecht, vol. 3, pp. 1-59, 1974.
    • (1974) Comm. Math. Inst. , vol.3 , pp. 1-59
  • 10
    • 84939320731 scopus 로고
    • Normal forms for singularities of nonlinear ordinary differential equations
    • R. Glowinski and J. L. Lions, eds. North Holland
    • S. Ushiki, “Normal forms for singularities of nonlinear ordinary differential equations, in Computing Methods in Applied Science and Engineering, VI, R. Glowinski and J. L. Lions, eds. North Holland, 1984.
    • (1984) Computing Methods in Applied Science and Engineering, VI
    • Ushiki, S.1
  • 11
    • 84859564559 scopus 로고
    • Existence d'attracteurs étranges dans le déploiement d'une singularité dégénérée d'un champ de vecteurs invariant par translation
    • Série I
    • S. Ushiki, H. Oka, and H. Kokubu, “Existence d'attracteurs étranges dans le déploiement d'une singularité dégénérée d'un champ de vecteurs invariant par translation,” C.R. Acad. Sc. Paris, t. 298, Série I, no. 3, pp. 39-42, 1984.
    • (1984) C.R. Acad. Sc. Paris , vol.298 , Issue.3 , pp. 39-42
    • Ushiki, S.1    Oka, H.2    Kokubu, H.3
  • 12
    • 84941457667 scopus 로고
    • Normal forms for constrained nonlinear differential equations-Part I: Theory and examples
    • Mem. ERL M87/83, Electron. Res. Lab., Univ. of California, Berkeley, CA, 94720 September 15
    • L. O. Chua and H. Oka, “Normal forms for constrained nonlinear differential equations-Part I: Theory and examples,” Mem. ERL M87/83, Electron. Res. Lab., Univ. of California, Berkeley, CA, 94720 September 15, 1987.
    • (1987)
    • Chua, L.O.1    Oka, H.2
  • 13
    • 0004030281 scopus 로고
    • 2nd edition, Reading, MA: Addison-Wesley
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    • (1971) Linear Algebra
    • Lang, S.1
  • 16
    • 0002776472 scopus 로고
    • Nilpotent normal forms and representation theory of sl(2)
    • (M. Golubitsky and J. Guckenheimer, Eds.) Contemporary Math., AMS
    • R. Cushman and J. Sanders, “Nilpotent normal forms and representation theory of sl(2)” in Multiparameter Bifurcation Theory, (M. Golubitsky and J. Guckenheimer, Eds.) Contemporary Math., vol. 56, AMS, 1986, pp. 31-51.
    • (1986) Multiparameter Bifurcation Theory , vol.56 , pp. 31-51
    • Cushman, R.1    Sanders, J.2
  • 17
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    • A simple global characterization for normal forms of singular vector fields
    • C. Elphick, E. Tirapegui, M. E. Brachet, P. Coullet, and G. Iooss, “A simple global characterization for normal forms of singular vector fields,” Physica, vol. 29D, pp. 95-127, 1987.
    • (1987) Physica , vol.29 D , pp. 95-127
    • Elphick, C.1    Tirapegui, E.2    Brachet, M.E.3    Coullet, P.4    Iooss, G.5
  • 18
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    • Perturbation Methods, Bifurcation Theory and Computer Algebra
    • Springer-Verlag
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    • (1987) Appl. Math. Sci. , vol.65
    • Rand, R.H.1    Armbruster, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.