A Fast Shadowing Algorithm for High Dimensional ODE Systems
Wayne Hayes and Kenneth R. Jackson
Abstract
A true trajectory of a chaotic dynamical system lying near an
approximate trajectory is called a shadow. Finding
shadows of numerical trajectories of ODE systems is very compute
intensive, and until recently it has been infeasible to study shadows of
higher-dimensional systems. We study the shadowing
algorithm introduced by Grebogi, Hammel, Yorke and Sauer in 1990 and
extended to arbitrary Hamiltonian systems by Quinlan and Tremaine in 1992,
and introduce several major optimizations resulting in
speedups of over 100. This algorithm is used to shadow
gravitational N-body systems with 150 phase space dimensions.
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