Subharmonic Solutions Near an Equilibrium Point for Hamiltonian Systems
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WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES
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This document studies subharmonic solutions near an equilibrium point for a Hamiltonian system. On the linear part of the system we impose a condition expressed in terms of its symplectic invariants. The higher order term is assumed to be superquadratic near the equilibrium point, and we show that this condition can be reduced to the center manifold. We transform the Hamiltonian system to a variational problem and we apply a minimax argument to find critical points. Keywords Hamiltonian matrices.
- Theoretical Mathematics