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On the Qualitative Behaviour of Symplectic Integrators. Part III. Perturbed Integrable Systems

✍ Scribed by Daniel Stoffer

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 278 KB
Volume: 217
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5729

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✦ Synopsis

We consider a dissipative perturbation of an integrable Hamiltonian system. The perturbed system is assumed to admit a weakly attractive invariant torus. The system is integrated with a symplectic integrator. The discrete system also admits an attractive invariant torus for sufficiently small step-sizes. The step-size may be much larger than the perturbation parameter; it has only to be logarithmically small compared to the perturbation parameter.

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