Email this article The Computational Complexity of the Initial Value Problem for the Three Body Problem
- Authors: Vasiliev N.N.1, Pavlov D.A.2
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Affiliations:
- St.Petersburg Department of Steklov Institute of Mathematics, St.Petersburg Electrotechnical University
- Institute of Applied Astronomy of the Russian Academy of Sciences
- Issue: Vol 224, No 2 (2017)
- Pages: 221-230
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239529
- DOI: https://doi.org/10.1007/s10958-017-3407-3
- ID: 239529
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Abstract
The paper is concerned with the computational complexity of the initial value problem (IVP) for a system of ordinary dynamical equations. A formal problem statement 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 the analysis of oscillatory solutions of the Sitnikov problem, which have a complex dynamical behavior. These solutions contradict the existence of an algorithm that solves the IVP in polynomial time. Bibliography: 12 titles.
About the authors
N. N. Vasiliev
St.Petersburg Department of Steklov Institute of Mathematics, St.Petersburg Electrotechnical University
Author for correspondence.
Email: vasiliev@pdmi.ras.ru
Russian Federation, St.Petersburg
D. A. Pavlov
Institute of Applied Astronomy of the Russian Academy of Sciences
Email: vasiliev@pdmi.ras.ru
Russian Federation, St.Petersburg
