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Rotation numbers and Lyapunov stability of elliptic periodic solutions. (English) Zbl 1161.37041

The stability of elliptic-type periodic solutions is investigated for the Hill (sometimes also called Jacobi) equations. Lower bounds of related rotation numbers are established on the basis of earlier results of the second author. Twist periodic solutions are proved for two different classes of Newtonian equations, one being regular and another singular.

MSC:

37J25 Stability problems for finite-dimensional Hamiltonian and Lagrangian systems
34D20 Stability of solutions to ordinary differential equations
37E40 Dynamical aspects of twist maps
34C25 Periodic solutions to ordinary differential equations
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