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SN~ (~6) lff 2It 3k_~ , 5 ",,x_J {b)

SN~ (~6) lff 2It 3k_~ , 5 ",,x_J {b)

References 78

References 78 C.D.Andereck, S.S.Liu, and H.L.Swinney [1986]. Flow regimes in a circular Couette system with independently rotating cylinders, J. Fluid Mech. 164, 155-183. D.Armbruster and G.Dangelmayr [ 1987]. Coupled stationary bifurcations in non- flux boundary value problems, Math. Proc. Camb. Phil. Soc. 101 167-192. T.B.Benjamin [1978]. Bifurcation phenomena in steady flows of a viscous fluid, Proc. R. Soc. London A 359 1-26, 27-43. T.B.Benjamin and F.Ursell [1954]. The stability of the plane free surface of a liquid in vertical periodic motion, Proc. R. Soc. London A 255 505-517. P.Chossat, Y.Demay, and G.Iooss [1987]. Interactions des modes azimutaux dans le probl~me de Couette-Taylor, Arch. Rational Mech. Anal. 99 213-248. S.Ciliberto and J.Gollub [1985a]. Chaotic mode competition in parametrically forced surface waves, J. Fluid Mech. 158 381-398. S.Ciliberto and J.Gollub [1985b]. Phenomenological model of chaotic mode competition in surface waves, Nuovo Cimento60 309-316. J.D.Crawford, M.Golubitsky, and E.Knobloch [1989]. In preparation. J.D.Crawford, E.Knobtoch, and H.Riecke [1989]. Competing parametric instabilities with circular symmetry, Phys. Lett A 135 20-24. G.Dangelmayr and D.Armbruster [1986]. Steady state mode interactions in the presence of O(2) symmetry and in non-flux boundary conditions. In Multiparameter Bifurcation Theory (eds. M.Golubitsky and J.Guckenheimer), Contemp. Math. 56, Amer. Math. Soc., Providence. G.Dangelmayr and E.Knobloch [1987]. The Takens-Bogdanov bifurcation with 0(2) symmetry, Phil. Trans. R. Soc. Lond. A322 243-279. P.G.Drazin [1975]. On the effects of sidewalls on Bdnard convection, Z. angew. Math. Phys. 27, 239-243. Z.C.Feng and P.R.Sethna [1989]. Symmetry-breaking bifurcations in resonant surface waves, J. Fluid Mech. 199 495-518. M.J.Field, M.Golubitsky, and I.N.Stewart [1990]. Bifurcations on hemispheres, preprint, Univ. of Houston. H.Fujii, M.Mimura, and Y.Nishiura [1982]. A picture of the global bifurcation diagram in ecological interacting and diffusing systems, Physica 5D 1-42. M.Golubitsky and W.F.Langford [1988]. Pattern formation and bistability in flow between counterrotating cylinders, Physica 32D 362-392. M.Golubitsky, J.E.Marsden, and D.G.Schaeffer [1984]. Bifurcation problems with hidden symmetries, in Partial Differential Equations and Dynamical Systems (ed. W.E.Fitzgibbon III), Research Notes in Math. 101, Pitman, San Francisco, 181-210. M.Golubitsky and I.N.Stewart [1986]. Symmetry and stability in Taylor-Couette flow, SlAM J. Math. Anal. 17 249-288. M.Golubitsky, I.N.Stewart, and D.G.Schaeffer [1988]. Singularities and Groups in Bifurcation Theory vol. II, Applied Math. Sci. 69, Springer, New York.

79 M.G.M. Gomes [1989]. Steady-state mode interactions in rectangular domains, M.Sc. thesis, Univ. of Warwick. P.Hall and I.C.Walton [1977]. The smooth transition to a convective r6gime in a two- dimensional box, Proc. R. Soc. Lond. A 358 199-221. L.M.Hocking [1987]. The damping of capillary-gravity waves at a rigid boundary, J. Fluid Mech. 179 253-266. G.W.Hunt [1982]. Symmetries of elastic buckling, Eng. Struct. 4 21-28. G.Iooss [1986]. Secondary bifurcations of Taylor vortices into wavy inflow and outflow boundaries, J. Fluid Mech. 173 273-288. E.Meron and I.Procaccia [19816]. Low dimensional chaos in surface waves: theoretical analysis of an experiment, Phys. Rev. A 34 3221-3237. T.Mullin [1982]. Cellular mutations in Taylor flow, J. Fluid Mech. 121 207-218. D.G.Schaeffer [1980]. Qualitative analysis of a model for boundary effects in the Taylor problem, Math. Proc. Camb. Phil. Soc. 87 307-337. M.Silber and E.Knobloch [1989]. Parametrically excited surface waves in square geometry, Phys. Len. A 137 349-354. F.Simonelli and J.Gollub [1989]. Surface wave mode interactions: effects of symmetry and degeneracy, J. Fluid Mech. 199 471-494. G.I.Taylor [1923]. Stability of a viscous liquid contained between two rotating cylinders, Phil. Trans. R. Soc. Lond. A 223 289-343. M.Umeki and T.Kambe [1989]. Nonlinear dynamics and chaos in parametrically excited surface waves, J. Phys. Soc. Japan 58 140-154.

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