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Rotation numbers and Lyapunov stability of elliptic periodic solutions
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.