DDA 36th Meeting, 10-14 April 2005
Session 13 The Quest for Precision
Oral, Wednesday, April 13, 2005, 3:05-5:45pm

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[13.02] Symplectic Integration Methods and Chaos: Timestep Selection and Lyapunov Time

W.I. Newman, A.Y. Lee (UCLA)

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

The author(s) of this abstract have provided an email address for comments about the abstract: win@ucla.edu

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