The stability of subharmonic solutions for Hamiltonian systems
The paper is devoted to the stability of subharmonic solutions of non-autonomous Hamiltonian systems. Under some natural conditions on the Hamiltonian, using the dual Morse index theory, the author obtains an (infinite) sequence of geometrically distinct periodic solutions. Peculiarities of these solutions are: Every element has at most one direction of instability, which in turn implies that at least \(2n-2\) Floquet multipliers are lying on the unit circle in the complex plane if the periodic solution is nondegenerate or all its \(2n\) Floquet multipliers are lying on the unit circle if the periodic solution is degenerate.
scientific article; zbMATH DE number 1417578