ACTION-ANGLE VARIABLES NEAR DEGENERATE PERIODIC ORBITS

Classical Floquet theory describes motion near a periodic orbit. However, there is a missing piece in the Floquet solution. A different Jordan normal form allows the decoupling of modal dynamics near the periodic orbit, and not just on the periodic orbit. A new eigenvector solution is offered in the case of repeated eigenvalues. This solution extends the Floquet decomposition to adjacent trajectories, and is fully canonical. This also yields the matrix of frequency partial derivatives, extending the solution's validity. Some numerical examples are offered.