| Autor: |
Derunova, E., Sapronov, Yu. |
| Zdroj: |
Russian Mathematics; Aug2015, Vol. 59 Issue 8, p9-18, 10p |
| Abstrakt: |
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 and normal forms of the principal part of the key functions. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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