TY - JOUR

T1 - Lyapunov Functions and Asymptotics at Infinity of Solutions of Equations that are Close to Hamiltonian Equations

AU - Sultanov, O. A.

PY - 2021/10/1

Y1 - 2021/10/1

N2 - We consider a nonlinear nonautonomous system of two ordinary differential equations with a stable fixed point and assume that the non-Hamiltonian part of the system tends to zero at infinity. We examine the asymptotic behavior of a two-parameter family of solutions that start from a neighborhood of the stable equilibrium. The proposed construction of asymptotic solutions is based on the averaging method and the transition in the original system to new dependent variables, one of which is the angle of the limit Hamiltonian system, and the other is the Lyapunov function for the complete system.

AB - We consider a nonlinear nonautonomous system of two ordinary differential equations with a stable fixed point and assume that the non-Hamiltonian part of the system tends to zero at infinity. We examine the asymptotic behavior of a two-parameter family of solutions that start from a neighborhood of the stable equilibrium. The proposed construction of asymptotic solutions is based on the averaging method and the transition in the original system to new dependent variables, one of which is the angle of the limit Hamiltonian system, and the other is the Lyapunov function for the complete system.

KW - 34D05

KW - 34D20

KW - 34E05

KW - asymptotics

KW - averaging

KW - Lyapunov function

KW - nonlinear differential equation

UR - http://www.scopus.com/inward/record.url?scp=85115240773&partnerID=8YFLogxK

U2 - 10.1007/s10958-021-05538-5

DO - 10.1007/s10958-021-05538-5

M3 - Article

AN - SCOPUS:85115240773

VL - 258

SP - 97

EP - 109

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -