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

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Abstract

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 ℝ6 and normal forms of the principal part of the key functions.

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Authors and Affiliations

  1. Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006, Russia

    E. V. Derunova & Yu. I. Sapronov

Authors
  1. E. V. Derunova
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  2. Yu. I. Sapronov
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Correspondence to E. V. Derunova.

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Original Russian Text © E.V. Derunova, Yu.I. Sapronov, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 8, pp. 14–24.

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Derunova, E.V., Sapronov, Y.I. Application of normalized key functions in a problem of branching of periodic extremals. Russ Math. 59, 9–18 (2015). https://doi.org/10.3103/S1066369X15080022

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  • DOI: https://doi.org/10.3103/S1066369X15080022

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