Counting symmetry-breaking solutions to symmetric variational problems
type: Item
instance of: scholarly article
title: Counting symmetry-breaking solutions to symmetric variational problems
zbMATH Open document ID: 0847.58017
DOI: 10.1007/BF02082945
author: Giuseppe Gaeta
published in: International Journal of Theoretical Physics
publication date: 1996-10-14T00:00:00Z
review text: The author develops a geometric theory of the action of a compact Lie group \(G\) on a finite-dimensional smooth manifold \(M\). For equivariant dynamical systems \(\dot x = f(x)\) \((f(gx)+\) \(dg \cdot f)(x))\) in variational case these results allow to apply the Ljusternik-Schnirelman category for obtaining the lower bound on the number of solutions with given symmetry \(H \subseteq G\). Concerning the ``equivariant branching lemma'', see also the works [Sov. Math., Dokl. 20, 586-590 (1979); translation from Dokl. Akad. Nauk SSSR 246, 1048-1051 (1979; Zbl 0429.47028)] and [``Branching theory of solutions of nonlinear equations under group invariance conditions'', Tashkent, ``Fan'' (1985; Zbl 0593.58028)] by the reviewer.
Mathematics Subject Classification ID: 58E09
zbMATH DE Number: 859293
zbMATH Keywords: isotropy subgroup
zbMATH Keywords: orbit space
zbMATH Keywords: stratum
zbMATH Keywords: symmetry breaking solutions
zbMATH Keywords: Lyusternik-Shnirelman category
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 859293