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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 448, Pages 80–95 (Mi znsl6304)  
Computational complexity of the initial value problem for the three-body problem

N. N. Vasilievab, D. A. Pavlovc

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg Electrotechnical University "LETI", St. Petersburg, Russia
c Institute of Applied Astronomy Russian Academy of Sciences, St. Petersburg, Russia
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Abstract: 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.
Key words and phrases: computational complexity, Turing machine, initial value problem, three-body problem, oscillatory motion.
Funding agency Grant number
Russian Science Foundation 14-11-00581
Received: 17.10.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 224, Issue 2, Pages 221–230
DOI: https://doi.org/10.1007/s10958-017-3407-3
Bibliographic databases:
Document Type: Article
UDC: 510.52+517.911+517.912
Language: Russian
Citation: N. N. Vasiliev, D. A. Pavlov, “Computational complexity of the initial value problem for the three-body problem”, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Zap. Nauchn. Sem. POMI, 448, POMI, St. Petersburg, 2016, 80–95; J. Math. Sci. (N. Y.), 224:2 (2017), 221–230
Citation in format AMSBIB
\Bibitem{VasPav16}
\by N.~N.~Vasiliev, D.~A.~Pavlov
\paper Computational complexity of the initial value problem for the three-body problem
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXVII
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 448
\pages 80--95
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6304}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3576250}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 2
\pages 221--230
\crossref{https://doi.org/10.1007/s10958-017-3407-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019675284}
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