Abstract
We apply average-case complexity theory to physical problems modeled by continuous-time dynamical systems. The computational complexity when simulating such systems for a bounded time-frame mainly stems from trajectories coming close to complex of the system. We show that if for most initial values the trajectories do not come close to the simulation can be done in polynomial time on average. For Hamiltonian systems we relate this to the volume of almost singularities in phase space and give some general criteria to show that a Hamiltonian system can be simulated efficiently on average. As an application we show that the planar circular-restricted three-body problem is average-case polynomial-time computable.
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