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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ZNSL_2016_448_a4,
     author = {N. N. Vasiliev and D. A. Pavlov},
     title = {Computational complexity of the initial value problem for the three-body problem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {80--95},
     publisher = {mathdoc},
     volume = {448},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a4/}
}
TY  - JOUR
AU  - N. N. Vasiliev
AU  - D. A. Pavlov
TI  - Computational complexity of the initial value problem for the three-body problem
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 80
EP  - 95
VL  - 448
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a4/
LA  - ru
ID  - ZNSL_2016_448_a4
ER  - 
%0 Journal Article
%A N. N. Vasiliev
%A D. A. Pavlov
%T Computational complexity of the initial value problem for the three-body problem
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 80-95
%V 448
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a4/
%G ru
%F ZNSL_2016_448_a4
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/