A theorem first put forth with respect to this problem states that a conformal one-to-one transformation from an annulus to itself that advances points on the outer edge positively and inner edge negatively has at least two fixed points.
The existence of Arnold diffusion in this problem was shown by Zhihong Xia. A theorem first put forth with respect to this problem states that a conformal one-to-one transformation from an annulus to itself that advances points on the outer edge positively and inner edge negatively has at least two fixed points. That theorem was proposed by Poincaré and proven by Birkhoff. Karl Sundman found a solution to this problem in terms of a uniformly convergent infinite series. Jacobi's work on it yielded his namesake integral. One of the first solutions to this problem is applied to the Trojan asteroids located at the Lagrange points of Jupiter. It is often considered in a version where one mass is negligible and all masses are moving in the same plane, which is the circular restricted version. For 10 points, name this unsolved problem first considered by Newton with respect to the movement of the Moon under the influences of the Sun and Earth.
The existence of Arnold diffusion in this problem was shown by Zhihong Xia.
three-body problem