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Volumn 10, Issue 5, 1997, Pages 1115-1150

Codimension-three unfoldings of reflectionally symmetric planar vector fields

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EID: 0000868937     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/10/5/007     Document Type: Article
Times cited : (28)

References (40)
  • 1
    • 0002945544 scopus 로고
    • Loss of stability of self-oscillation close to resonance and versal deformations of equivariant vector fields
    • [Ar77] Arnol'd V I 1977 Loss of stability of self-oscillation close to resonance and versal deformations of equivariant vector fields Funkts. Anal. Priliozh. 11 2-10 Arnol'd V I 1977 Functional Anal. Appl. 11 85-92 (Engl. Transl.)
    • (1977) Funkts. Anal. Priliozh. , vol.11 , pp. 2-10
    • Arnol'd, V.I.1
  • 2
    • 0002945544 scopus 로고
    • Engl. Transl.
    • [Ar77] Arnol'd V I 1977 Loss of stability of self-oscillation close to resonance and versal deformations of equivariant vector fields Funkts. Anal. Priliozh. 11 2-10 Arnol'd V I 1977 Functional Anal. Appl. 11 85-92 (Engl. Transl.)
    • (1977) Functional Anal. Appl. , vol.11 , pp. 85-92
    • Arnol'd, V.I.1
  • 9
    • 0001520664 scopus 로고
    • A survey of quadratic systems
    • [Co66] Coppel WA 1966 A survey of quadratic systems J. Diff. Eqns 2 293-304
    • (1966) J. Diff. Eqns , vol.2 , pp. 293-304
    • Coppel, W.A.1
  • 10
    • 0002907911 scopus 로고
    • Some quadratic systems with at most one limit cycle
    • ed U Kirchgraber and H O Walther (New York: Wiley)
    • [Co89] Coppel W A 1989 Some quadratic systems with at most one limit cycle Dynamics Reported vol 2 ed U Kirchgraber and H O Walther (New York: Wiley) 61-88
    • (1989) Dynamics Reported , vol.2 , pp. 61-88
    • Coppel, W.A.1
  • 13
    • 0000095998 scopus 로고    scopus 로고
    • Hilbert's 16th problem for quadratic vector fields and finite cyclicity of elementary graphics
    • [DER95] Dumortier F, El Morsalani M and Rousseau C 1996 Hilbert's 16th problem for quadratic vector fields and finite cyclicity of elementary graphics Nonlinearity 9 1209-61
    • (1996) Nonlinearity , vol.9 , pp. 1209-1261
    • Dumortier, F.1    El Morsalani, M.2    Rousseau, C.3
  • 14
    • 43949161677 scopus 로고
    • Hilbert's 16th problem for quadratic vector fields
    • [DRR94] Dumortier F, Roussarie R and Rousseau C 1994 Hilbert's 16th problem for quadratic vector fields J. Diff. Eqns 110 86-133
    • (1994) J. Diff. Eqns , vol.110 , pp. 86-133
    • Dumortier, F.1    Roussarie, R.2    Rousseau, C.3
  • 16
    • 0012144124 scopus 로고
    • On some bifurcations of equilibria with a zero and a pair of purely imaginary eigenvalues
    • ed E A Leontovich-Andronova Gor'kov Gos. Univ. Gorr'kij (in Russian)
    • [Ga78] Gavrilov N K 1978 On some bifurcations of equilibria with a zero and a pair of purely imaginary eigenvalues Methods of the Qualitative Theory of Differential Equations ed E A Leontovich-Andronova Gor'kov Gos. Univ. Gorr'kij (in Russian) pp 33-40
    • (1978) Methods of the Qualitative Theory of Differential Equations , pp. 33-40
    • Gavrilov, N.K.1
  • 17
    • 0041609746 scopus 로고
    • On some bifurcations of equilibria of codimension two of divergence-free vector fields
    • Gor'kov Gos. Univ. Gorr'kij (in Russian)
    • [Ga85] Gavrilov NK 1985 On some bifurcations of equilibria of codimension two of divergence-free vector fields Methods of the Qualitative Theory of Differential Equations Gor'kov Gos. Univ. Gorr'kij (in Russian) pp 46-55
    • (1985) Methods of the Qualitative Theory of Differential Equations , pp. 46-55
    • Gavrilov, N.K.1
  • 18
    • 0043112545 scopus 로고
    • On bifurcations of equilibria with a zero and a pair of purely imaginary eigenvalues with an additional degeneracy
    • Gor'kov Gos. Univ. Gorr'kij (in Russian)
    • [Ga87] Gavrilov N K 1987 On bifurcations of equilibria with a zero and a pair of purely imaginary eigenvalues with an additional degeneracy Methods of the Qualitative Theory of Differential Equations Gor'kov Gos. Univ. Gorr'kij (in Russian) pp 43-51
    • (1987) Methods of the Qualitative Theory of Differential Equations , pp. 43-51
    • Gavrilov, N.K.1
  • 22
    • 0013101248 scopus 로고
    • Infinite period bifurcation and global bifurcation branches
    • [Ke81] Keener J P 1981 Infinite period bifurcation and global bifurcation branches SIAM J. Appl. Math. 41 127-44
    • (1981) SIAM J. Appl. Math. , vol.41 , pp. 127-144
    • Keener, J.P.1
  • 23
    • 0001609913 scopus 로고
    • Minimal model of binary fluid convection
    • [KM90] Knobloch E and Moore D R 1990 Minimal model of binary fluid convection Phys. Rev. A 42 4693-709
    • (1990) Phys. Rev. A , vol.42 , pp. 4693-4709
    • Knobloch, E.1    Moore, D.R.2
  • 24
    • 0010310306 scopus 로고
    • The bifurcation set for the 1 : 4 resonance problem
    • [Kra94] Krauskopf B 1994 The bifurcation set for the 1 : 4 resonance problem Experimental Mathematics 3 107-28
    • (1994) Experimental Mathematics , vol.3 , pp. 107-128
    • Krauskopf, B.1
  • 26
    • 0040600586 scopus 로고    scopus 로고
    • Bifurcations at ∞ in a model for 1 : 4 resonance
    • [Kra97] Krauskopf B 1997 Bifurcations at ∞ in a model for 1 : 4 resonance Erg. Theor. Dyn. Syst. 17(4)
    • (1997) Erg. Theor. Dyn. Syst. , vol.17 , Issue.4
    • Krauskopf, B.1
  • 27
  • 28
    • 0018505697 scopus 로고
    • Periodic and steady-state mode interactions lead to tori
    • [La79] Langford W H 1979 Periodic and steady-state mode interactions lead to tori SIAM. J. Appl. Math. 37 22-18
    • (1979) SIAM. J. Appl. Math. , vol.37 , pp. 22-118
    • Langford, W.H.1
  • 29
    • 0002333747 scopus 로고
    • A review of interactions of Hopf and steady-state bifurcations
    • ed Barenblatt, Iooss and Joseph (Boston, MA: Pitman)
    • [La83] Langford W H 1983 A review of interactions of Hopf and steady-state bifurcations Nonlinear Dynamics and Turbulence ed Barenblatt, Iooss and Joseph (Boston, MA: Pitman) pp 215-37
    • (1983) Nonlinear Dynamics and Turbulence , pp. 215-237
    • Langford, W.H.1
  • 31
    • 0042611668 scopus 로고
    • Multiple instabilities in rotating convection
    • [Mor90] Moroz I M 1990 Multiple instabilities in rotating convection Geophys. Astrophys. Fluid Dynamics 53 183-204
    • (1990) Geophys. Astrophys. Fluid Dynamics , vol.53 , pp. 183-204
    • Moroz, I.M.1
  • 33
    • 0000576441 scopus 로고
    • Unusual time-dependent phenomena in Taylor-Couette flow at moderately low Reynolds numbers
    • [MCP87] Mullin T, Cliffe K A and Pfister G 1987 Unusual time-dependent phenomena in Taylor-Couette flow at moderately low Reynolds numbers Phys. Rev. Lett. 58 2212-15
    • (1987) Phys. Rev. Lett. , vol.58 , pp. 2212-2215
    • Mullin, T.1    Cliffe, K.A.2    Pfister, G.3
  • 34
    • 84956105054 scopus 로고
    • An experimental and numerical study of a codimension-2 bifurcation in a rotating annulus
    • [MTC89] Mullin T, Tavener S J and Cliffe K A 1989 An experimental and numerical study of a codimension-2 bifurcation in a rotating annulus Europhys. Lett. 8 251-6
    • (1989) Europhys. Lett. , vol.8 , pp. 251-256
    • Mullin, T.1    Tavener, S.J.2    Cliffe, K.A.3
  • 35
    • 84968514049 scopus 로고
    • Algebraic integrals, integrability and the problem of the centre
    • [Schlo93] Schlomiuk D 1993 Algebraic integrals, integrability and the problem of the centre Trans. AMS 338 799-841
    • (1993) Trans. AMS , vol.338 , pp. 799-841
    • Schlomiuk, D.1
  • 36
    • 0028496424 scopus 로고
    • Laser with injected signal: Perturbation of an invariant circle
    • [SO94] Solari H G and Oppo G-L 1994 Laser with injected signal: Perturbation of an invariant circle Opt. Commun. 111 173-190
    • (1994) Opt. Commun. , vol.111 , pp. 173-190
    • Solari, H.G.1    Oppo, G.-L.2
  • 37
    • 51649178043 scopus 로고
    • Singularities of vector fields
    • [Ta74a] Takens F 1974 Singularities of vector fields Publ. Math. IHES 43 47-100
    • (1974) Publ. Math. IHES , vol.43 , pp. 47-100
    • Takens, F.1
  • 38
    • 0002529372 scopus 로고    scopus 로고
    • The limited effectiveness of normal forms: A critical review and extension of local bifurcation studies of the Brusselator PDE
    • [WH97] Wittenberg R W and Holmes P 1997 The limited effectiveness of normal forms: A critical review and extension of local bifurcation studies of the Brusselator PDE Physica D 100 1-40
    • (1997) Physica D , vol.100 , pp. 1-40
    • Wittenberg, R.W.1    Holmes, P.2
  • 39
    • 84956229471 scopus 로고
    • On the versality of a family of symmetric vector fields on the plane
    • [Zo84] Zoła̧dek H 1984 On the versality of a family of symmetric vector fields on the plane Math. USSR Sbornik 48 463-98
    • (1984) Math. USSR Sbornik , vol.48 , pp. 463-498
    • Zoła̧dek, H.1
  • 40
    • 0000813963 scopus 로고
    • Quadratic systems with centres and their perturbations
    • [Zo94] Zoła̧dek H 1994 Quadratic systems with centres and their perturbations J. Diff. Eqns 109 223-73
    • (1994) J. Diff. Eqns , vol.109 , pp. 223-273
    • Zoła̧dek, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.