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Linearized stability and instability of nonconstant periodic solutions of Lagrangian equations
Author(s) -
Zhang Meirong,
Cen Xiuli,
Cheng Xuhua
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4935
Subject(s) - mathematics , instability , stability (learning theory) , lagrangian , mathematical analysis , stability criterion , physics , mechanics , computer science , statistics , discrete time and continuous time , machine learning
This paper is motivated by the stability problem of nonconstant periodic solutions of time‐periodic Lagrangian equations, like the swing and the elliptic Sitnikov problem. As a beginning step, we will study the linearized stability and instability of nonconstant periodic solutions that are bifurcated from those of autonomous Lagrangian equations. Applying the theory for Hill equations, we will establish a criterion for linearized stability. The criterion shows that the linearized stability depends on the temporal frequencies of the perturbed systems in a delicate way.