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Volumn 163, Issue 1, 2002, Pages 1-33

Hamiltonian Hopf bifurcation with symmetry

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EID: 0036017442     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050200182     Document Type: Article
Times cited : (14)

References (34)
  • 2
  • 3
    • 0003285219 scopus 로고
    • Differential forms in algebraic topology
    • [BT82] Springer-Verlag
    • [BT82] BOTT, R. AND TU, L. [1982]: Differential Forms in Algebraic Topology. Graduate Texts in Mathematics, vol. 82. Springer-Verlag.
    • (1982) Graduate Texts in Mathematics , vol.82
    • Bott, R.1    Tu, L.2
  • 5
    • 0000639077 scopus 로고
    • Bifurcation of periodic solutions near a collision of eigenvalues of opposite signature
    • [Bri90]
    • [Bri90] BRIDGES, T. J. [1990]: Bifurcation of periodic solutions near a collision of eigenvalues of opposite signature. Math. Proc. Camb. Phil. Soc. 108, 575-601.
    • (1990) Math. Proc. Camb. Phil. Soc. , vol.108 , pp. 575-601
    • Bridges, T.J.1
  • 6
    • 0001511509 scopus 로고
    • n with application to plane Poiseuille flow
    • [Bri90a]
    • n with application to plane Poiseuille flow Arch. Rational Mech. Anal 106, 335-376
    • (1990) Arch. Rational Mech. Anal. , vol.106 , pp. 335-376
    • Bridges, T.J.1
  • 8
    • 0003300445 scopus 로고    scopus 로고
    • Methods in equivariant bifurcations and dynamical systems
    • [ChL00] World Scientific
    • [ChL00] CHOSSAT, P. AND LAUTERBACH, L. [2000]: Methods in Equivariant bifurcations and Dynamical Systems. Advanced Ser. in Nonlinear Dyn. 15, World Scientific.
    • (2000) Advanced Ser. in Nonlinear Dyn. , vol.15
    • Chossat, P.1    Lauterbach, L.2
  • 10
    • 0000894149 scopus 로고
    • Genetic bifurcation of hamiltonian vector fields with symmetry
    • [DMM92]
    • [DMM92] DELLNITZ, M., MELBOURNE, I. & MARSDEN, J. E. [1992]: Genetic Bifurcation of Hamiltonian vector fields with symmetry. Nonlinearity 5, 979-996.
    • (1992) Nonlinearity , vol.5 , pp. 979-996
    • Dellnitz, M.1    Melbourne, I.2    Marsden, J.E.3
  • 11
    • 0030101770 scopus 로고    scopus 로고
    • Symmetry breaking for compact Lie groups
    • [Fi94]
    • [Fi94] FIELD, M. [1996]: Symmetry breaking for compact Lie groups, Memoirs of the American Math. Soc. 120.
    • (1996) Memoirs of the American Math. Soc. , vol.120
    • Field, M.1
  • 12
    • 0013248064 scopus 로고
    • The Bénard problem, symmetry & the lattice of isotropy subgroups
    • [G83] Bruter, C. P. et al. (eds.), Reidel
    • [G83] GOLUBITSKY, M. [1983]: The Bénard Problem, symmetry & the lattice of isotropy subgroups. In Bifurcation Theory, Mechanics & Physics. Bruter, C. P. et al. (eds.), pp. 225-256. Reidel.
    • (1983) Bifurcation Theory, Mechanics & Physics , pp. 225-256
    • Golubitsky, M.1
  • 13
    • 0001855683 scopus 로고
    • The constrained Liapunov-Schmidt procedure and periodic orbits
    • [GMSD95] Normal Forms and Homoclinic Chaos, LANGFORD, W. F. AND NAGATA, W. eds.
    • [GMSD95] GOLUBITSKY, M., MARSDEN, J. E., STEWART, I. & DELLNITZ, M. [1995]: The constrained Liapunov-Schmidt procedure and periodic orbits. In Normal Forms and Homoclinic Chaos, pages 81-127. LANGFORD, W. F. AND NAGATA, W. eds. Fields Institute Communications, 4.
    • (1995) Fields Institute Communications , vol.4 , pp. 81-127
    • Golubitsky, M.1    Marsden, J.E.2    Stewart, I.3    Dellnitz, M.4
  • 15
    • 0021853542 scopus 로고
    • Hopf bifurcation in the presence of symmetry
    • [GoSt85]
    • [GoSt85] GOLUBITSKY, M. AND STEWART, I. [1985]: Hopf bifurcation in the presence of symmetry. Arch. Rational Mech. Anal. 87, 107-165.
    • (1985) Arch. Rational Mech. Anal. , vol.87 , pp. 107-165
    • Golubitsky, M.1    Stewart, I.2
  • 16
    • 0001454797 scopus 로고
    • Generic bifurcation of Hamiltonian systems with symmetry
    • [GoS87] With an appendix by J. E. MARSDEN
    • [GoS87] GOLUBITSKY, M. AND STEWART, I.: With an appendix by J. E. MARSDEN [1987]: Generic bifurcation of Hamiltonian systems with symmetry. Physica D 24, 391-405.
    • (1987) Physica D , vol.24 , pp. 391-405
    • Golubitsky, M.1    Stewart, I.2
  • 18
    • 0000328613 scopus 로고
    • A Hopf bifurcation with spherical symmetry
    • [HRS92]
    • [HRS92] HAAF, H., ROBERTS, M., STEWART, I. [1992]: A Hopf bifurcation with spherical symmetry. ZAMP 43, 793-826.
    • (1992) ZAMP , vol.43 , pp. 793-826
    • Haaf, H.1    Roberts, M.2    Stewart, I.3
  • 19
    • 0003198090 scopus 로고
    • Introduction to Lie algebras and representation theory
    • [Hu72] Springer-Verlag
    • [Hu72] HUMPHREYS, J. E. [1972]: Introduction to Lie Algebras and Representation Theory. Graduate Texts in Mathematics, no. 9. Springer-Verlag.
    • (1972) Graduate Texts in Mathematics , vol.9
    • Humphreys, J.E.1
  • 20
    • 0001599254 scopus 로고
    • Hopf bifurcation in the presence of spherical symmetry: Analytical results
    • [IoRo89]
    • [IoRo89] IOOSS, G., ROSSI, M. [1989]: Hopf bifurcation in the presence of spherical symmetry: analytical results. SIAM J. Math. Anal. 20, 511-532.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 511-532
    • Iooss, G.1    Rossi, M.2
  • 22
    • 0030394634 scopus 로고    scopus 로고
    • Branches of stable three-tori using Hamiltonian methods in Hopf bifurcation on a rhombic lattice
    • [KMS96]
    • [KMS96] KINK, V., MARSDEN, J. E. & SILBER, M. [1996]: Branches of stable three-tori using Hamiltonian methods in Hopf bifurcation on a rhombic lattice. Dynamics and Stability of Systems 11, (4), 267-302.
    • (1996) Dynamics and Stability of Systems , vol.11 , Issue.4 , pp. 267-302
    • Kink, V.1    Marsden, J.E.2    Silber, M.3
  • 24
    • 0003166049 scopus 로고    scopus 로고
    • Hopf bifurcations in systems with spherical symmetry, Part I
    • [Le97]
    • [Le97] LEIS, C. [1997]: Hopf bifurcations in systems with spherical symmetry, part I. Documenta Mathematica 2, 61-113.
    • (1997) Documenta Mathematica , vol.2 , pp. 61-113
    • Leis, C.1
  • 25
    • 84976180597 scopus 로고
    • Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group
    • [MD93]
    • [MD93] MELBOURNE, I. & DELLNITZ, M. [1993]: Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. Math. Proc. Camb. Phil. Soc. 114, 235-268.
    • (1993) Math. Proc. Camb. Phil. Soc. , vol.114 , pp. 235-268
    • Melbourne, I.1    Dellnitz, M.2
  • 26
    • 0000594324 scopus 로고
    • Bibliographical notes on generic bifurcation in Hamiltonian systems
    • [Mey86] Multiparameter Bifurcation Theory, (American Mathematical Society)
    • [Mey86] MEYER, K. R. [1986]: Bibliographical notes on generic bifurcation in Hamiltonian systems. In Multiparameter Bifurcation Theory, Contemp. Math. no. 56 (American Mathematical Society), 373-381.
    • (1986) Contemp. Math. , vol.56 , pp. 373-381
    • Meyer, K.R.1
  • 27
    • 0002052233 scopus 로고
    • 4 for mass ratios near the critical mass ratio of Routh
    • [MeyS71]
    • 4 for mass ratios near the critical mass ratio of Routh. Celestial Mech. 4, 99-109.
    • (1971) Celestial Mech. , vol.4 , pp. 99-109
    • Meyer, K.R.1    Schmidt, D.S.2
  • 28
    • 0001572622 scopus 로고
    • Periodic solutions near equilibria of symmetric Hamiltonian systems
    • [MRS88]
    • [MRS88] MONTALDI, J. A., ROBERTS, R. M. & STEWART, I. N. [1988]: Periodic solutions near equilibria of symmetric Hamiltonian systems. Phil. Trans. R. Soc. Lond. A 325, 237-293
    • (1988) Phil. Trans. R. Soc. Lond. A , vol.325 , pp. 237-293
    • Montaldi, J.A.1    Roberts, R.M.2    Stewart, I.N.3
  • 29
    • 84974249274 scopus 로고
    • Hopf bifurcation for equivariant conservative and time-reversible systems
    • [Vbw90]
    • [Vbw90] VANDERBAUWHEDE, A. [1990]: Hopf bifurcation for equivariant conservative and time-reversible systems. Proc. Roy. Soc. Edinburgh Sect. A 116, 103-128.
    • (1990) Proc. Roy. Soc. Edinburgh Sect. A , vol.116 , pp. 103-128
    • Vanderbauwhede, A.1
  • 30
    • 0002341726 scopus 로고
    • General reduction method for periodic solutions near equilibria
    • [VvdM95] Normal Forms and Homoclinic Chaos, LANGFORD, W. F. & NAGATA, W. eds.
    • [VvdM95] VANDERBAUWHEDE, A. & VAN DER MEER, J. C. [1995]: General reduction method for periodic solutions near equilibria. In Normal Forms and Homoclinic Chaos, pages 273-294. LANGFORD, W. F. & NAGATA, W. eds. Fields Institute Communications, 4.
    • (1995) Fields Institute Communications , vol.4 , pp. 273-294
    • Vanderbauwhede, A.1    Van der Meer, J.C.2
  • 31
    • 0003349147 scopus 로고
    • The Hamiltonian Hopf bifurcation
    • [vdM85] Springer Verlag
    • [vdM85] VAN DER MEER, J. C. [1985]: The Hamiltonian Hopf Bifurcation. Lecture Notes in Mathematics 1160. Springer Verlag.
    • (1985) Lecture Notes in Mathematics , vol.1160
    • Van der Meer, J.C.1
  • 32
    • 0001203818 scopus 로고
    • Hamiltonian Hopf bifurcation with symmetry
    • [vdM90]
    • [vdM90] VAN DER MEER, J. C. [1990]: Hamiltonian Hopf bifurcation with symmetry. Nonlinearity 3, 1041-1056.
    • (1990) Nonlinearity , vol.3 , pp. 1041-1056
    • Van der Meer, J.C.1
  • 33
    • 0013247434 scopus 로고    scopus 로고
    • Degenerate Hamiltonian Hopf bifurcations
    • [vdM96] Conservative Systems and Quantum Chaos, BATES, L. M. & ROD, D. L., eds.
    • [vdM96] VAN DER MEER, J. C. [1996]: Degenerate Hamiltonian Hopf bifurcations. In Conservative Systems and Quantum Chaos, pp. 159-176. BATES, L. M. & ROD, D. L., eds. Fields Institute Communications, 8.
    • (1996) Fields Institute Communications , vol.8 , pp. 159-176
    • Van der Meer, J.C.1
  • 34
    • 0001316020 scopus 로고
    • On the algebraic problem concerning the normal forms of linear dynamical systems
    • [Wil36]
    • [Wil36] WILLIAMSON, J. [1936]: On the algebraic problem concerning the normal forms of linear dynamical systems. Amer. J. Math. 58, 141-163.
    • (1936) Amer. J. Math. , vol.58 , pp. 141-163
    • Williamson, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.