コロキウム

Moeckel [1] gave sufficient conditions for the existence of transition orbits near the collinear equilibrium point L2 of the planer circular restricted three-body problem (PCR3BP) under fixed energy conditions using a variational method for the Maupertui functional. From the result of Easton [2], Moeckel also pointed out that the existence of the transition orbit allows the evaluation of the cohomology of an isolated invariant set on its energy level set. We apply Moeckel's result to potential systems motivated by saddle centers to give an evaluation of the cohomology of the isolated invariant sets. We also give another sufficient condition for the previous potential system and the PCR3BP using a variational method for the Lagrange functionals. In this talk, we will present these results. This is joint work with my supervisor, Assoc. Prof. Mitsuru Shibayama.

[1] R. Moeckel, A variational proof of existence of transit orbits in the restricted three-body problem, Dynamical Systems, 20(1):45-58, 2005.
[2] R.W. Easton, Existence of invariant sets inside a submanifold convex to the flow, Journal of Differential Equations, 7:54-68, 1970.