The three-body problem was attacked by Vladimir Arnold and Jurgen Moser with the so-called KAM theorem, named after their initials and that of Andrei Kolmogorov, who in 1954 had provided the guidelines for its treatment. Henri Poincaré had already addressed the problem at the end of the 19th century, highlighting the chaotic behavior of their solutions depending on small changes in the initial conditions, intuiting that the problem was linked to number theory and, in particular, to small divisors with large coefficients. The solution found by the KAM was that for small perturbations, almost all orbits are stable. That is, they are not exactly periodic, but remain close to the periodic orbits of the unperturbed system, and are therefore called “quasi-periodic.” This confirms what Isaac Newton wrote in Proposition III.10 of Principia Mathematica: “The motion of the planets in the heavens can be maintained for a very long time.” (It may seem trivial, but Henri Poincaré has shown that it isn’t at all.)
