Bifurcation of the state of equilibrium of an oscillator with nonlinear restoring force of Third order

Periodic perturbations of the oscillator + x 3 + ax = 0, a 2 < 8, are considered. Smallness of perturbations is governed by the smallness of the neighborhood of the state of equilibrium x = 0 and by a small positive parameter. Conditions are given that ensure that an invariant two-dimensional tor...

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Bibliographic Details
Published in:Vestnik, St. Petersburg University. Mathematics St. Petersburg University. Mathematics, 2015-04, Vol.48 (2), p.57-60
Main Authors: Bibikov, Yu. N., Pliss, V. A.
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:Periodic perturbations of the oscillator + x 3 + ax = 0, a 2 < 8, are considered. Smallness of perturbations is governed by the smallness of the neighborhood of the state of equilibrium x = 0 and by a small positive parameter. Conditions are given that ensure that an invariant two-dimensional torus branches from the equilibrium when the small parameter passes through the zero value.
ISSN:1063-4541
1934-7855
DOI:10.3103/S106345411502003X