Rotation numbers and Lyapunov stability of elliptic periodic solutions | Zendy

Jifeng Chu | Zendy; Meirong Zhang | Zendy

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Rotation numbers and Lyapunov stability of elliptic periodic solutions

Author(s) -

Jifeng Chu,

Meirong Zhang

Publication year - 2008

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2008.21.1071

Subject(s) - twist , mathematics , nonlinear system , mathematical analysis , lyapunov function , class (philosophy) , rotation (mathematics) , rotation number , scalar (mathematics) , pure mathematics , lyapunov stability , physics , geometry , computer science , quantum mechanics , artificial intelligence

Using the relation between the Hill's equations and the Ermakov- Pinney equations established by Zhang (27), we will give some interesting lower bounds of rotation numbers of Hill's equations. Based on the Birkhofi normal forms and the Moser twist theorem, we will prove that two classes of nonlinear, scalar, time-periodic, Newtonian equations will have twist periodic solutions, one class being regular and another class being singular.

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