# zbMATH — the first resource for mathematics

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
##### Keywords:
tori; bifurcation; critical point; Morse critical orbit; group action
Full Text:
##### References:
 [1] B. A. Strukov and A. P. Levanyuk, Physical Foundations of Ferroelectric Phenomena in Crystals [in Russian], Nauka, Moscow 1995. · Zbl 0899.00012 [2] B. M. Darinskii and Yu. I. Sapronov, Izv. Vyssh. Uchebn. Zaved., Ser. Mat.,41, No. 2, 35–46 (1997) [3] Yu. I. Sapronov, Usp. Mat. Nauk,51, No. 1, 101–132 (1996). [4] D. Siersma, Quart. J. Math. Oxford Ser. (2),32, No. 125, 119–127 (1981). · Zbl 0449.58008 · doi:10.1093/qmath/32.1.119 [5] V. I. Arnold, A. N. Varchenko, and S. M. Gussein-Zade, Singularities of Differentiable Maps. Vol. I. The Classification of Critical Points, Caustics, and Wave Fronts, Birkhauser, Boston, 1985. [6] Yu. I. Sapronov, Mat. Sb.,180, No. 10, 1299–1310 (1989). [7] A. V. Gnezdilov, Pontryagin Readings-VIII, Abstracts Voronezh, Voronezh State University, 1997, p. 36. [8] A. V. Gnezdilov, Trudy Matem. Fakul’teta VGU (Novaya Seriya),2, (18), 19–26 (1997).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.