Dynamic bifurcation problems with E.Schmidt spectrum in the linearization under group symmetry conditions
B.V. Loginov; I.V. Konopleva; L.V. Mironova1
| Annotation | Results of the articles \cite{Konopleva1}, \cite{Konopleva2} for stationary problems of branching theory with E. Schmidt spectrum in the linearization are transformating on dynamic bifurcation problems on E. Schmidt spectrum. On the base of general theorem on the group symmetry theorem on the group symmetry of nonlinear problems inheritance by the relevant branching equations and branching equations in the root-subspaces (BEqRs), moving along bifurcation point trajectory implicit operators theorem under group symmetry conditions and theorem on BEqRs reduction by the number of equations in the case of variational BEqRs are proved. Terminology and notations of the works \cite{Trenogin3}-- \cite{Sidor6} are used. |
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| Keywords | Dynamic bifurcation problems, Poincar\`{e}-Andronov-Hopf bifurcation; E. Schmidt spectrum, group symmetry, $G$-invariant implicit operator theorem, variational type branching equations in the root-subspaces. |
1Professor, Ulyanovsk State Technical University, Ulyanovsk; loginov@ulstu.ru
2Docent, Ulyanovsk State Technical University, Ulyanovsk; i.konopleva@ulstu.ru
3Assistent,Ulyanovsk Higher Civil Aviation School, Ulyanovsk;
Citation: B.V. Loginov; I.V. Konopleva; L.V. Mironova, "[Dynamic bifurcation problems with E.Schmidt spectrum in the linearization under group symmetry conditions]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,14:1 (2012) 25–35 (In Russian)
