A Stable Manifold Theorem for Degenerate Fixed Points with Applications to Celestial Mechanics
Richard McGehee
Journal of Differential Equations 14 (1973), 497-513. doi: 10.1016/0022-0396(73)90077-6
Note. Parabolic orbits in certain celestial mechanics systems can be viewed as the stable and unstable manifolds to a degenerate periodic orbit at infinity. The stable and unstable manifolds are shown to be real analytic for these systems.
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Copies can be downloaded from the publisher's Web site: doi: 10.1016/0022-0396(73)90077-6