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November  2008, 21(4): 1071-1094. doi: 10.3934/dcds.2008.21.1071

Rotation numbers and Lyapunov stability of elliptic periodic solutions

Jifeng Chu 1, and  Meirong Zhang 2,

1. 

College of Science, Hohai University, Nanjing 210098, China
2. 

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received  March 2007 Revised  March 2008 Published  May 2008

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 Birkhoff 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.
Keywords: Ermakov-Pinney equation, twist coefficient., periodic solution, Lyapunov stability, rotation number, Hill's equation.
Mathematics Subject Classification: Primary 37J25; Secondary 34D20, 37E40, 34C2.
Citation: Jifeng Chu, Meirong Zhang. Rotation numbers and Lyapunov stability of elliptic periodic solutions. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1071-1094. doi: 10.3934/dcds.2008.21.1071
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