Geodesic
Application of normalized key functions in a~problem of branching of periodic extremals
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2015), pp. 14-24

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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.
Keywords: Fredholm functionals, extremals, circular symmetry, resonance, Lyapunov–Schmidt method.
Mots-clés : bifurcation 
@article{IVM_2015_8_a1,
     author = {E. V. Derunova and Yu. I. Sapronov},
     title = {Application of normalized key functions in a~problem of branching of periodic extremals},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {14--24},
     publisher = {mathdoc},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_8_a1/}
}
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E. V. Derunova; Yu. I. Sapronov. Application of normalized key functions in a~problem of branching of periodic extremals. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2015), pp. 14-24. http://geodesic.mathdoc.fr/item/IVM_2015_8_a1/