메뉴 건너뛰기




Volumn 155, Issue 1, 1999, Pages 44-72

Genericity conditions for finite cyclicity of elementary graphics

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033542306     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3570     Document Type: Article
Times cited : (10)

References (25)
  • 3
    • 0000495631 scopus 로고
    • On the number of limit cycles appearing with variations of coefficients from an equilibrium state of the type of a focus or a center
    • Bautin N. N. On the number of limit cycles appearing with variations of coefficients from an equilibrium state of the type of a focus or a center. Mat. Sb. 30:1952;181-196.
    • (1952) Mat. Sb. , vol.30 , pp. 181-196
    • Bautin N., N.1
  • 4
    • 0000095998 scopus 로고    scopus 로고
    • Hilbert's 16th problem for quadratic systems and cyclicity of elementary graphics
    • Dumortier F., El Morsalani M., Rousseau C. Hilbert's 16th problem for quadratic systems and cyclicity of elementary graphics. Nonlinearity. 9:1996;1209-1261.
    • (1996) Nonlinearity , vol.9 , pp. 1209-1261
    • Dumortier, F.1    El Morsalani, M.2    Rousseau, C.3
  • 6
    • 0001237461 scopus 로고
    • Elementary graphics of cyclicity one and two
    • Dumortier F., Roussarie R., Rousseau C. Elementary graphics of cyclicity one and two. Nonlinearity. 7:1994;1001-1043.
    • (1994) Nonlinearity , vol.7 , pp. 1001-1043
    • Dumortier, F.1    Roussarie, R.2    Rousseau, C.3
  • 7
    • 0001554506 scopus 로고    scopus 로고
    • Perturbations of graphics with semi-hyperbolic singularities
    • El Morsalani M. Perturbations of graphics with semi-hyperbolic singularities. Bull. Sci. Math. 120:1996;337-366.
    • (1996) Bull. Sci. Math. , vol.120 , pp. 337-366
    • El Morsalani, M.1
  • 9
    • 84957312349 scopus 로고
    • Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
    • Il'yashenko Yu., Yakovenko S. Finitely-smooth normal forms of local families of diffeomorphisms and vector fields. Russian Math. Surveys. 46:1991;1-43.
    • (1991) Russian Math. Surveys , vol.46 , pp. 1-43
    • Il'yashenko, Yu.1    Yakovenko, S.2
  • 10
    • 0002015513 scopus 로고
    • Finite cyclicity of elementary polycycles in generic families
    • Providence: Amer. Math. Soc. p. 21-95
    • Il'yashenko Yu., Yakovenko S. Finite cyclicity of elementary polycycles in generic families. Amer. Math. Soc. Transl. Ser. 2. 1995;Amer. Math. Soc. Providence. p. 21-95.
    • (1995) Amer. Math. Soc. Transl. Ser. 2
    • Il'yashenko, Yu.1    Yakovenko, S.2
  • 11
    • 0000474566 scopus 로고
    • Generalized Hopf bifurcation and its dual: Generalized homoclinic bifurcation
    • Joyal P. Generalized Hopf bifurcation and its dual: generalized homoclinic bifurcation. SIAM J. Appl. Math. 48:1988;481-496.
    • (1988) SIAM J. Appl. Math. , vol.48 , pp. 481-496
    • Joyal, P.1
  • 12
    • 0009257472 scopus 로고
    • Cycles of dynamical systems in the plane and Rolle's theorem
    • Khovanskii A. Cycles of dynamical systems in the plane and Rolle's theorem. Siberian Math. J. 25:1984;502-506.
    • (1984) Siberian Math. J. , vol.25 , pp. 502-506
    • Khovanskii, A.1
  • 13
    • 0000606003 scopus 로고
    • Real analytic varieties with the property of finiteness and complex Abelian integrals
    • Khovanskii A. Real analytic varieties with the property of finiteness and complex Abelian integrals. Funct. Anal. Appl. 18:1984;40-50.
    • (1984) Funct. Anal. Appl. , vol.18 , pp. 40-50
    • Khovanskii, A.1
  • 15
    • 0001646745 scopus 로고
    • On few-parameter generic families of vector fields on the two-dimensional sphere
    • Providence: Amer. Math. Soc. p. 155-201
    • Kotova A., Stanzo V. On few-parameter generic families of vector fields on the two-dimensional sphere. Amer. Math. Soc. Transl. Ser. 2. 1995;Amer. Math. Soc. Providence. p. 155-201.
    • (1995) Amer. Math. Soc. Transl. Ser. 2
    • Kotova, A.1    Stanzo, V.2
  • 16
    • 0002635906 scopus 로고
    • Une démonstration du théorème de division pour les fonctions différentiables
    • Lassalle M. G. Une démonstration du théorème de division pour les fonctions différentiables. Topology. 12:1973;41-62.
    • (1973) Topology , vol.12 , pp. 41-62
    • Lassalle M., G.1
  • 17
    • 0000924578 scopus 로고
    • Théorie de Khovanskii et problème de Dulac
    • Moussu R., Roche C. Théorie de Khovanskii et problème de Dulac. Invent. Math. 105:1991;431-441.
    • (1991) Invent. Math. , vol.105 , pp. 431-441
    • Moussu, R.1    Roche, C.2
  • 18
    • 0001309891 scopus 로고
    • Cyclicité finie des polycycles hyperboliques des champs de vecteurs du plan: Mise sous forme normale
    • Mourtada A. Cyclicité finie des polycycles hyperboliques des champs de vecteurs du plan: Mise sous forme normale. Lecture Notes in Mathematics. 1455:1990;272-314.
    • (1990) Lecture Notes in Mathematics , vol.1455 , pp. 272-314
    • Mourtada, A.1
  • 19
    • 0002089448 scopus 로고
    • Degenerate and non-trivial hyperbolic polycycles with two vertices
    • Mourtada A. Degenerate and non-trivial hyperbolic polycycles with two vertices. J. Differential Equations. 113:1994;68-83.
    • (1994) J. Differential Equations , vol.113 , pp. 68-83
    • Mourtada, A.1
  • 20
    • 0001491171 scopus 로고
    • Degenerate and non-trivial hyperbolic 2-polycycles: Two independant Ecalle-Roussarie compensators and Khovanskii's theory
    • El Morsalani M., Mourtada A. Degenerate and non-trivial hyperbolic 2-polycycles: Two independant Ecalle-Roussarie compensators and Khovanskii's theory. Nonlinearity. 7:1994;1593-1604.
    • (1994) Nonlinearity , vol.7 , pp. 1593-1604
    • El Morsalani, M.1    Mourtada, A.2
  • 22
    • 51249171477 scopus 로고
    • On the number of limit cycles which appear by perturbation of a separatrix loop of planar vector fields
    • Roussarie R. On the number of limit cycles which appear by perturbation of a separatrix loop of planar vector fields. Bol. Soc. Brasil. Mat. 17:1986;67-101.
    • (1986) Bol. Soc. Brasil. Mat. , vol.17 , pp. 67-101
    • Roussarie, R.1
  • 23
    • 0000776081 scopus 로고
    • A note on finite cyclicity and Hilbert's 16th problem
    • New York/Berlin: Springer-Verlag. p. 161-168
    • Roussarie R. A note on finite cyclicity and Hilbert's 16th problem. Lecture Notes in Mathematics. 1988;Springer-Verlag, New York/Berlin. p. 161-168.
    • (1988) Lecture Notes in Mathematics
    • Roussarie, R.1
  • 24
    • 36149036159 scopus 로고
    • Cyclicité finie des lacets et des points cuspidaux
    • Roussarie R. Cyclicité finie des lacets et des points cuspidaux. Nonlinearity. 2:1989;73-117.
    • (1989) Nonlinearity , vol.2 , pp. 73-117
    • Roussarie, R.1
  • 25
    • 0032048419 scopus 로고    scopus 로고
    • Cyclicity of graphics with semi-hyperbolic points inside quadratic systems
    • Rousseau C., Świrszcz G., Żoła̧dek H. Cyclicity of graphics with semi-hyperbolic points inside quadratic systems. J. Dynam. Control Systems. 4:1998;149-189.
    • (1998) J. Dynam. Control Systems , vol.4 , pp. 149-189
    • Rousseau, C.1    Świrszcz, G.2    Zoła̧dek, H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.