Geodesic
Computational complexity of the initial value problem for the three-body problem
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 80-95
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The paper deals with the computational complexity of the initial value problem (IVP) for a system of ordinary dynamical equations. A formal statement of the problem is given, containing a Turing machine with an oracle for getting the initial values as real numbers. It is proven that the computational complexity of the IVP for the three-body problem is not bounded by a polynomial. The proof is based on oscillatory solutions for the Sitnikov problem that have complex dynamical behavior. These solutions prevent the existence of an algorithm that solves the IVP in polynomial time. 
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N. N. Vasiliev; D. A. Pavlov. Computational complexity of the initial value problem for the three-body problem. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 80-95. http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a4/

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