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- W2911462004 abstract "The main focus of this thesis is the dynamics of a two-degree-of-freedom Hamiltoniansystem near an elliptic equilibrium point in 1 : ±2 resonance, as described by its integrableresonant normal form approximation. After applying singular reduction, the system isstudied on the reduced phase space that Kummer called the orbit manifold. We give acomplete description of the critical values of the energy–momentum mapping which thanenables us to study the topology of the regular, and more importantly, the singular fibres.We then derive equations for the period of the reduced system, for the rotation numberand the non-trivial action. Although some of these results are not new, our approachdoes not rely on compact fibration and is based on a similar approach introduced earlierby S. Vũ Ngoc for focus–focus points. The non-trivial action of the system enables us toestablish fractional monodromy very elegantly by deriving the transition matrix for theactions directly. Both the isoenergetic non-degeneracy condition and the Kolmogorovnon-degeneracy condition of KAM theory are derived and analysed for the resonant case.It tuns out that the twist vanishes in a neighbourhood of the equilibrium point for thesign-indefinite case. The Kolmogorov condition, however, is always satisfied near 1 : ±2resonant equilibria. [Continues.]" @default.
- W2911462004 created "2019-02-21" @default.
- W2911462004 creator A5075332426 @default.
- W2911462004 date "2008-01-01" @default.
- W2911462004 modified "2023-09-27" @default.
- W2911462004 title "Resonant elliptic equilibria in Hamiltonian systems" @default.
- W2911462004 hasPublicationYear "2008" @default.
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