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Imperfect bifurcation in the presence of symmetry. (English) Zbl 0467.58019


MSC:

37G99 Local and nonlocal bifurcation theory for dynamical systems
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
58K35 Catastrophe theory

Citations:

Zbl 0409.58007
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References:

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[10] McLeod, J.B., Sattinger, D.H.: Loss of stability at a double eigenvalue. J. Funct. Anal.14, 62-84 (1973) · Zbl 0275.47045
[11] Poènaru, V.: SingularitésC ? en présence de symétrie, Lecture notes in mathematics, Vol. 510. Berlin, Heidelberg, New York: Springer 1976
[12] Poston, T., Stewart, I.: Catastrophe theory and its applications. San Francisco: Pitman 1978 · Zbl 0382.58006
[13] Sattinger, D.H.: Group representation theory and branch points of non-linear functional equations. SIAM J. Math. Anal.8, 179-201 (1977) · Zbl 0396.47040
[14] Sattinger, D.H.: Group representation theory, bifurcation theory, and pattern formation. (To appear) · Zbl 0416.47027
[15] Sattinger, D.H.: Spontaneous symmetry breaking in nonlinear problems. In: Bifurcation theory and applications in Scientific disciplines. (eds. O. Gurel, O. E. Rössler). The New York Academy of Sciences, New York 1979 · Zbl 0447.58016
[16] Schaeffer, D., Golubitsky, M.: Bifurcation analysis near a double eigenvalue of a model chemical reaction. Arch. Rat. Mech. Anal. (to appear) · Zbl 0522.35010
[17] Schaeffer, D., Golubitsky, M.: Boundary conditions and mode jumping in the buckling of a rectangular plate. Commun. Math. Phys. (to appear) · Zbl 0414.73036
[18] Schecter, S.: Bifurcations with symmetry. In: The Hopf bifurcation and its applications. Marsden, J.E., McCracken, M. (eds.). Appl. Math. Sci., Vol. 19, pp. 224-249. Berlin, Heidelberg, New York: Springer 1976
[19] Schwarz, G.: Smooth functions invariant under the action of a compact Lie group. Topology14, 63-68 (1975) · Zbl 0297.57015
[20] Thompson, J.M.T., Hunt, G.W.: A general theory of elastic stability. London: Wiley 1973 · Zbl 0351.73066
[21] Thompson, J.M.T.: Catastrophe theory and its role in applied mechanics. In: Theoretical and applied mechanics. Koiter, W.T. (ed.), pp. 451-458. Amsterdam, Oxford, New York: North-Holland 1976
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