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Volumn 129, Issue 3-4, 1999, Pages 171-202

Takens-Bogdanov bifurcation on the hexagonal lattice for double-layer convection

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EID: 0346072477     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00007-X     Document Type: Article
Times cited : (38)

References (25)
  • 1
    • 0001947201 scopus 로고
    • The 2:1 steady-Hopf mode interaction in the two-layer Bénard problem
    • K. Fujimura, Y. Renardy, The 2:1 steady-Hopf mode interaction in the two-layer Bénard problem, Physica D 85 (1995) 25-65.
    • (1995) Physica D , vol.85 , pp. 25-65
    • Fujimura, K.1    Renardy, Y.2
  • 2
    • 0024072031 scopus 로고
    • Bifurcating solutions at the onset of convection in the Benard problem of two fluids
    • M. Renardy, Y. Renardy, Bifurcating solutions at the onset of convection in the Benard problem of two fluids, Physica D 32 (1988) 227-252.
    • (1988) Physica D , vol.32 , pp. 227-252
    • Renardy, M.1    Renardy, Y.2
  • 4
    • 0028051257 scopus 로고
    • On the Hopf bifurcation occurring in the two-layer Rayleigh-Bénard convective instability
    • P. Colinet, J.C. Legros, On the Hopf bifurcation occurring in the two-layer Rayleigh-Bénard convective instability, Phys. Fluids 6 (1994) 2631-2639 .
    • (1994) Phys. Fluids , vol.6 , pp. 2631-2639
    • Colinet, P.1    Legros, J.C.2
  • 5
    • 0030523791 scopus 로고    scopus 로고
    • Pattern formation for oscillatory bulk-mode competition in a two-layer Bénard problem
    • Y. Renardy, Pattern formation for oscillatory bulk-mode competition in a two-layer Bénard problem, Zeitschr. fuer Angew. Math. u. Phy. 47 (1996) 567-590.
    • (1996) Zeitschr. fuer Angew. Math. U. Phy. , vol.47 , pp. 567-590
    • Renardy, Y.1
  • 7
    • 0029698680 scopus 로고    scopus 로고
    • Double-layer convection: A brief review and some recent experimental results
    • Advances in Multi-Fluid Flows, Y. Renardy, A.V. Coward, D. Papageorgiou, S.-M. Sun (Eds.), Society for Industrial and Applied Mathematics
    • F.H. Busse, G. Sommermann, Double-layer convection: a brief review and some recent experimental results, Advances in Multi-Fluid Flows, Proc. of the 1995 AMS-IMS-SIAM Joint Summer Res. Conf. on Multi-Fluid Flows and Interfacial Instabilities, in: Y. Renardy, A.V. Coward, D. Papageorgiou, S.-M. Sun (Eds.), Society for Industrial and Applied Mathematics, 1996, pp. 33-41.
    • (1996) Proc. of the 1995 AMS-IMS-SIAM Joint Summer Res. Conf. on Multi-Fluid Flows and Interfacial Instabilities , pp. 33-41
    • Busse, F.H.1    Sommermann, G.2
  • 8
    • 0029703065 scopus 로고    scopus 로고
    • Observations of time-dependent behavior in the two-layer Rayleigh-Benard system
    • paper Da.05, 19-21 November
    • C.D. Andereck, P.W. Colovas, M.M. Degen, Observations of time-dependent behavior in the two-layer Rayleigh-Benard system, paper Da.05, Annual Meeting of the American Physical Society Division of Fluid Dynamics, 19-21 November 1995, also in Advances in Multi- Fluid Flows, Proc. 1995 AMS-IMS-SIAM Joint Summer Res. Conf. on Analysis of Multi-Fluid Flows and Interfacial Instabilities, in: Y. Renardy, A.V. Coward, D. Papageorgiou, S.-M. Sun (Eds.), Society for Industrial and Applied Mathematics, 1996, pp. 3-12.
    • (1995) Annual Meeting of the American Physical Society Division of Fluid Dynamics
    • Andereck, C.D.1    Colovas, P.W.2    Degen, M.M.3
  • 9
    • 0029703065 scopus 로고    scopus 로고
    • Advances in Multi-Fluid Flows
    • Y. Renardy, A.V. Coward, D. Papageorgiou, S.-M. Sun (Eds.), Society for Industrial and Applied Mathematics
    • C.D. Andereck, P.W. Colovas, M.M. Degen, Observations of time-dependent behavior in the two-layer Rayleigh-Benard system, paper Da.05, Annual Meeting of the American Physical Society Division of Fluid Dynamics, 19-21 November 1995, also in Advances in Multi-Fluid Flows, Proc. 1995 AMS-IMS-SIAM Joint Summer Res. Conf. on Analysis of Multi-Fluid Flows and Interfacial Instabilities, in: Y. Renardy, A.V. Coward, D. Papageorgiou, S.-M. Sun (Eds.), Society for Industrial and Applied Mathematics, 1996, pp. 3-12.
    • (1996) Proc. 1995 AMS-IMS-SIAM Joint Summer Res. Conf. on Analysis of Multi-Fluid Flows and Interfacial Instabilities , pp. 3-12
  • 10
    • 0346474881 scopus 로고
    • Strong spatial interactions with 1:1 resonance: A three-layer convection problem
    • K.A. Julien, Strong spatial interactions with 1:1 resonance: a three-layer convection problem, Nonlinearity 7 (1995) 1655-1693.
    • (1995) Nonlinearity , vol.7 , pp. 1655-1693
    • Julien, K.A.1
  • 11
    • 0000898517 scopus 로고    scopus 로고
    • Hopf bifurcation on the hexagonal lattice with small frequency
    • M. Renardy, Hopf bifurcation on the hexagonal lattice with small frequency, Advan. in Diff. Eq. 1 (1996) 283-299.
    • (1996) Advan. in Diff. Eq. , vol.1 , pp. 283-299
    • Renardy, M.1
  • 12
    • 0000086032 scopus 로고
    • Time-periodic convection in Hele-Shaw slots: The diagonal oscillation
    • M.D. Graham, U. Müller, P.H. Steen, Time-periodic convection in Hele-Shaw slots: the diagonal oscillation, Phys. Fluids A 4 (1992) 2382-2393.
    • (1992) Phys. Fluids A , vol.4 , pp. 2382-2393
    • Graham, M.D.1    Müller, U.2    Steen, P.H.3
  • 13
    • 0038941172 scopus 로고
    • Oscillatory convection in binary mixtures
    • E. Knobloch, Oscillatory convection in binary mixtures, Phys. Rev. A 34 (1986) 1538-1549.
    • (1986) Phys. Rev. A , vol.34 , pp. 1538-1549
    • Knobloch, E.1
  • 15
    • 4244103350 scopus 로고
    • Chaotic dynamics in systems with square symmetry
    • J. Guckenheimer, D. Armbruster, S. Kim, Chaotic dynamics in systems with square symmetry, Phys Lett. A 140 (1989) 416-428.
    • (1989) Phys Lett. A , vol.140 , pp. 416-428
    • Guckenheimer, J.1    Armbruster, D.2    Kim, S.3
  • 16
    • 0000257676 scopus 로고
    • The Hopf bifurcation on a hexagonal lattice, Multiparameter Bifurcation Theory
    • M. Golubitsky, J.M. Guckenheimer (Eds.)
    • M. Roberts, J.W. Swift, D.H. Wagner, The Hopf bifurcation on a hexagonal lattice, Multiparameter Bifurcation Theory, in: M. Golubitsky, J.M. Guckenheimer (Eds.), AMS Series Contemp. Math., 56 (1986) pp. 283-318.
    • (1986) AMS Series Contemp. Math. , vol.56 , pp. 283-318
    • Roberts, M.1    Swift, J.W.2    Wagner, D.H.3
  • 18
    • 0346912293 scopus 로고
    • The Fuller index and global Hopf bifurcation
    • S.N. Chow, J. Mallet-Paret, The Fuller index and global Hopf bifurcation, J. Diff. Eq. 29 (1978) 66-85.
    • (1978) J. Diff. Eq. , vol.29 , pp. 66-85
    • Chow, S.N.1    Mallet-Paret, J.2
  • 19
    • 0347105112 scopus 로고    scopus 로고
    • Errata for [5], Zeitschr. fuer Angew. Math. u. Phys. 48 (1997) 171
    • Y. Renardy, Errata for [5], Zeitschr. fuer Angew. Math. u. Phys. 48 (1997) 171.
    • Renardy, Y.1
  • 20
    • 0000664495 scopus 로고
    • Bifurcation on the hexagonal lattice and the planar Bénard problem
    • E. Buzano, M. Golubitsky, Bifurcation on the hexagonal lattice and the planar Bénard problem, Phil. Trans. Roy. Soc. London A 308 (1983) 617-667.
    • (1983) Phil. Trans. Roy. Soc. London A , vol.308 , pp. 617-667
    • Buzano, E.1    Golubitsky, M.2
  • 22
  • 24
    • 0001409687 scopus 로고
    • Global bifurcation of periodic orbits
    • J.C. Alexander, J. Yorke, Global bifurcation of periodic orbits, Am. J. Math. 100 (1978) 263-292.
    • (1978) Am. J. Math. , vol.100 , pp. 263-292
    • Alexander, J.C.1    Yorke, J.2
  • 25
    • 0024611705 scopus 로고
    • A theoretical and experimental study of double-layer convection
    • S. Rasenat, F.H. Busse, I. Rehberg, A theoretical and experimental study of double-layer convection, J. Fluid Mech. 199 (1989) 519-540.
    • (1989) J. Fluid Mech. , vol.199 , pp. 519-540
    • Rasenat, S.1    Busse, F.H.2    Rehberg, I.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.