Sub-harmonics for two-dimensional Hamiltonian systems
The author proves the following result: Every asymptotically linear \(T\)-periodic Hamiltonian system in \(\mathbb{R}^2\) which has at least two periodic orbits must have infinitely many sub-harmonics, of course, in the presence of non-resonance conditions. The existence result is based on the Morse theory for the action developed by Conley and Zehnder. Note that the author's main result is strictly related to a recent result by Frank, proved by completely different methods.
scientific article; zbMATH DE number 1406548