Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 8, Pages 14–24
This article is cited in 2 scientific papers (total in 2 papers)
Application of normalized key functions in a problem of branching of periodic extremals
E. V. Derunova, Yu. I. Sapronov
Chair of Mathematical Modeling, Voronezh State University, 1 University sq., Voronezh, 394006 Russia
In this paper we construct a procedure of approximate calculation and analysis of branches of bifurcating solutions to a periodic variational problem. The goal of the work is a study of bifurcation of cycles in dynamic systems in cases of double resonances $1:2:3$, $1:2:4$, $p:q:p+q$ and others. An ordinary differential equation (ODE) of the sixth order is considered as a general model equation. Application of the Lyapunov–Schmidt method and transition to boundary and angular singularities allow to simplify a description of branches of extremals and caustics. Also we list systems of generators of algebraic invariants under an orthogonal semi-free action of the circle on $\mathbb R^6$ and normal forms of the main part of the key functions.
Fredholm functionals, extremals, circular symmetry, resonance, bifurcation, Lyapunov–Schmidt method.
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Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:8, 9–18
E. V. Derunova, Yu. I. Sapronov, “Application of normalized key functions in a problem of branching of periodic extremals”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 8, 14–24; Russian Math. (Iz. VUZ), 59:8 (2015), 9–18
Citation in format AMSBIB
\by E.~V.~Derunova, Yu.~I.~Sapronov
\paper Application of normalized key functions in a~problem of branching of periodic extremals
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\jour Russian Math. (Iz. VUZ)
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D. V. Kostin, “Initial-boundary value problems for Fuss-Winkler-Zimmermann and Swift-Hohenberg nonlinear equations of 4th order”, Mat. Vestn., 70:1 (2018), 26–39
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