Symplectic Integration Methods and Chaos: Timestep Selection and Lyapunov Time

Details Symplectic Integration Methods and Chaos: Timestep Selection and Lyapunov Time Symplectic Integration Methods and Chaos: Timestep Selection and Lyapunov Time

May 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005dda....36.1302n&link_type=abstract

American Astronomical Society, DDA meeting #36, #13.02; Bulletin of the American Astronomical Society, Vol. 37, p.531

Computer Science

Numerical Analysis

3

Scientific paper

Symplectic integration methods are popular topics of investigation in numerical analysis and dynamical systems theory. In general, they do not produce trajectories corresponding to some approximate Hamiltonian (Varadarajan, 1973; Lichtenberg & Lieberman, 1992) but reside ``close" to some approximate Hamiltonian for a time determined by the time step (Bennetin & Giorgili, 1994; Hairer & Lubich, 1997; Reich, 1999). The expression that emerges for this residency time resembles results in KAM theory for perturbed integrable systems which undergo a transition to chaos. Here, we explore the conjecture that the Lyapunov time for such artificial chaos scales in the same way as the residency time. This conclusion can be converted into a practical method for establishing whether chaotic behavior is physical or numerical

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