Авторы: N. N. Vasiliev, D. A. Pavlov
Журнал: Journal of Mathematical Sciences Volume 224, Issue 2
Информация о статье: https://link.springer.com/article/10.1007/s10958-017-3407-3
Текст статьи: https://arxiv.org/pdf/1704.08762.pdf
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.