# American Institute of Mathematical Sciences

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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

 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.
Citation: Jifeng Chu, Meirong Zhang. Rotation numbers and Lyapunov stability of elliptic periodic solutions. Discrete & Continuous Dynamical Systems - A, 2008, 21 (4) : 1071-1094. doi: 10.3934/dcds.2008.21.1071
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