TY - JOUR

T1 - Regular and singular periodic perturbations of an oscillator with cubic restoring force

AU - Bibikov, Yu N.

AU - Bukaty, V. R.

AU - Dorodenkov, A. A.

PY - 2010/6/1

Y1 - 2010/6/1

N2 - The paper considers small periodic regular and singular perturbations of a system, whose conservative part is an oscillator with cubic restoring force. The smallness of perturbations is due to both the smallness of the neighborhood of equilibrium and the presence of a small parameter. In the absence of a small parameter, we obtain conditions for Lyapunov stability of the equilibrium position. If a small parameter is present, we derive (both for regular and singular perturbations) an equation whose positive roots are in correspondence with invariant two-dimensional tori of the perturbed system.

AB - The paper considers small periodic regular and singular perturbations of a system, whose conservative part is an oscillator with cubic restoring force. The smallness of perturbations is due to both the smallness of the neighborhood of equilibrium and the presence of a small parameter. In the absence of a small parameter, we obtain conditions for Lyapunov stability of the equilibrium position. If a small parameter is present, we derive (both for regular and singular perturbations) an equation whose positive roots are in correspondence with invariant two-dimensional tori of the perturbed system.

KW - invariant tori

KW - singular perturbations

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=84859726900&partnerID=8YFLogxK

U2 - 10.3103/S1063454110020044

DO - 10.3103/S1063454110020044

M3 - Article

AN - SCOPUS:84859726900

VL - 43

SP - 82

EP - 91

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -