Application of normalized key functions in a problem of branching of periodic extremals

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....

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Bibliographic Details
Published in:Russian mathematics 2015-08, Vol.59 (8), p.9-18
Main Authors: Derunova, E. V., Sapronov, Yu. I.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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 generating algebraic invariants under an orthogonal semi-free action of the circle on ℝ 6 and normal forms of the principal part of the key functions.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X15080022