Y Kominis et al 2008 J. Phys. A: Math. Theor. 41 115202 doi:10.1088/1751-8113/41/11/115202
Explicit near-symplectic mappings of Hamiltonian systems with Lie-generating functions
Y Kominis1, K Hizanidis1, D Constantinescu2 and O Dumbrajs3,4
Show affiliationsThe construction of explicit near-symplectic mappings for generic Hamiltonian systems with the utilization of Lie transforms is presented. The method is mathematically rigorous and systematically extended to high order with respect to a perturbation parameter. The explicit mappings are compared to their implicit counterparts, which use mixed-variable generating functions, in terms of conservation of invariant quantities, calculation speed and accurate construction of Poincaré surfaces of sections. The comparative study considers a wide range of parameters and initial conditions for which different time scales are involved due to large differences between internal and external frequencies of the system.
- PACS
- MSC
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37J10 Symplectic mappings, fixed points
70H15 Canonical and symplectic transformations
37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion
- Subjects
- Dates
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Issue 11 (21 March 2008)
Received 20 November 2007, in final form 15 January 2008
Published 4 March 2008
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Explicit near-symplectic mappings of Hamiltonian systems with Lie-generating functions
Y Kominis et al 2008 J. Phys. A: Math. Theor. 41 115202
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