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Bifurcations of critical tori for functionals with 3-circular symmetry. (English. Russian original) Zbl 0985.37047
Funct. Anal. Appl. 34, No. 1, 67-69 (2000); translation from Funkts. Anal. Prilozh. 34, No. 1, 83-86 (2000).
Bifurcations of sets of critical points of a smooth functional defined on a Banach manifold \(M\) and invariant with respect to a smooth action of an \(m\)-dimensional torus have a wide range of applications. This paper deals with this problem in the case \(m=3\). In particular, the author gives a complete description of the bifurcation of Morse critical orbits from a point of minimum with a 3-circular pleat singularity.

MSC:
37G40 Dynamical aspects of symmetries, equivariant bifurcation theory
58K45 Singularities of vector fields, topological aspects
37G10 Bifurcations of singular points in dynamical systems
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