Solutions for degenerate Hamiltonian systems

Determine whether solutions analogous to those guaranteed by the KAM theorem exist for degenerate Hamiltonian systems that violate the non-degeneracy condition.

Background

The paper discusses the twist condition and the non-degeneracy criterion required for the standard KAM theorem. For nearly integrable Hamiltonian systems satisfying this criterion, the KAM theorem provides quasi-periodic solutions and invariant structures. The authors note that the corresponding situation for degenerate Hamiltonian systems, in which the criterion fails, is unresolved.