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Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields. (English) Zbl 0411.58013


MSC:

37G99 Local and nonlocal bifurcation theory for dynamical systems
37C75 Stability theory for smooth dynamical systems
34C29 Averaging method for ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
57R25 Vector fields, frame fields in differential topology
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[1] V. I. Arnol’d, ”Lectures on bifurcations and versal families,” Usp. Mat. Nauk,27, No. 5, 119-185 (1972).
[2] R. I. Bogdanov, ”Versal deformations of a singular point of a vector field on a plane in the case of zero eigenvalues,” Proceedings of the I. G. Petrovskii Seminar [in Russian], No. 2, Moscow State Univ. (1976), pp. 37-65.
[3] R. I. Bogdanov, ”Bifurcations of a limit cycle of one family of vector fields on a plane,” Proceedings of the I. G. Petrovskii Seminar [in Russian], No. 2, Moscow State Univ. (1976), pp. 23-35.
[4] A. D. Bryuno, ”Instability in a Hamiltonian system and the distribution of asteroids,” Mat. Sb.,83, 213-312 (1970). · Zbl 0266.34045
[5] R. J. Sacker, ”On invariant surfaces and bifurcation of periodic solutions of ordinary differential equations,” Report IMMNYU 333, New York Univ. (1964).
[6] R. J. Sacker, ”A new approach to the perturbation theory of invariant surfaces,” Commun. Pure Appl. Math.,18, No. 4, 717-732 (1965). · Zbl 0133.35501 · doi:10.1002/cpa.3160180409
[7] V. S. Kozyakin, ”Subfurcation of periodic oscillations,” Dokl. Akad. Nauk SSSR,232, No. 1, 25-27 (1977).
[8] S. Ya. Gertsenshtein and V. M. Shmidt, ”Nonlinear development and interaction of perturbations of finite amplitude under convective instability of a rotating flat layer,” Dokl. Akad. Nauk SSSR,225, No. 1, 59-62 (1975).
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