Estimation of the number of ultrasubharmonics for a two-dimensional almost autonomous Hamiltonian system periodic in time - Vakal, Yu. E.; Parasyuk, I. O. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
Using the Arnold method of detection of fixed points of symplectic diffeomorphisms, we find lower estimates for the number of ultrasubharmonics in a Hamiltonian system on a two-dimensional symplectic manifold with almost autonomous time-periodic Hamiltonian. We show that the asymptotic behavior of these estimates as the perturbation parameter tends to zero depends on which of the four zones of a ring domain foliated by closed level curves of the unperturbed Hamiltonian the generating unperturbed ultrasubharmonics belong to.