Estimation of the number of ultrasubharmonics for a two-dimensional almost autonomous Hamiltonian system periodic in time
| Autor: | I. O. Parasyuk, Yu. E. Vakal |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
General Mathematics
Mathematical analysis Fixed point Hamiltonian system symbols.namesake symbols Covariant Hamiltonian field theory Superintegrable Hamiltonian system Hamiltonian (quantum mechanics) Symplectomorphism Mathematics::Symplectic Geometry Symplectic manifold Symplectic geometry Mathematics |
| Zdroj: | Ukrainian Mathematical Journal. 64:525-554 |
| ISSN: | 1573-9376 0041-5995 |
| DOI: | 10.1007/s11253-012-0663-8 |
| Popis: | UDC 517.9 The Arnold method for the detection of fixed points of symplectic diffeomorphisms is used to establish lower estimates for the number of ultrasubharmonics in a Hamiltonian system on a two-dimensional symplectic manifold with an almost autonomous Hamiltonian periodic in time. It is shown that the asymptotic behavior of these estimates (as the small parameter of perturbation tends to zero) depends on the zone (from the set four zones of an annular domain foliated by the closed level curves of the unperturbed Hamiltonian) containing the generating unperturbed ultrasubharmonics. |
| Databáze: | OpenAIRE |
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