Estimation of the number of ultrasubharmonics for a two-dimensional almost autonomous Hamiltonian system periodic in time
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.
English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 4, pp 525-554.
Citation Example: Parasyuk I. O., Vakal Yu. E. Estimation of the number of ultrasubharmonics for a two-dimensional almost autonomous Hamiltonian system periodic in time // Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 463-489.