コロキウム

Using the variational method, Chenciner and Montgomery (2000) proved the existence of a figure-eight orbit in the planar three-body problem with equal masses. Since then, a number of solutions to the N-body problem have been discovered. The Sitnikov problem is a special case of the three-body problem. This system is known to be chaotic and has been studied using symbolic dynamics (J. Moser, 1973). In this talk, we study the limiting case of the Sitnikov problem. Using the variational method, we show the existence of various kinds of solutions in the planar Sitnikov problem. For a given symbolic sequence, we demonstrate the existence of orbits realizing it. We also prove the existence of periodic orbits and heteroclinic orbits connecting them. This is joint work with Yuika Kajihara and Guowei Yu.