A. A. Zevin
Abstract:
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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