Electron. J. Diff. Eqns., Vol. 1998(1998), No. 05, pp. 1-9.

On the prescribed-period problem for autonomous Hamiltonian systems

A. A. Zevin

Asymptotically quadratic and subquadratic autonomous Hamiltonian systems are considered. Lower bounds for the number of periodic solutions with a prescribed minimal period are obtained. These bounds are expressed in terms of the numbers of frequencies corresponding to the critical points of the Hamiltonian. Results are based on a global analysis of families of periodic solutions emanating from these points.

Submitted March 3, 1997. Published February 20, 1998.
Math Subject Classification: 58F14, 58F22.
Key Words: Autonomous Hamiltonian system, periodic solutions, global analysis, prescribed-period problem.

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A. A. Zevin
Transmag Research Institute, Ukrainian Academy of Sciences
320005 Dniepropetrovsk, Piesarzhevsky 5, Ukraine
e-mail address: zevin@transmag.vidr.dp.ua
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