Two-dimensional billiard systems are Turing complete: halting of any Turing machine is equivalent to a bounded trajectory entering a specified open set.
Variational approach to second species periodic solutions of poincaré of the three-body problem.Discrete and Continuous Dynamical Systems, 33(3):1009–1032
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Classical billiards can compute
Two-dimensional billiard systems are Turing complete: halting of any Turing machine is equivalent to a bounded trajectory entering a specified open set.