An abstract KAM theorem is developed for infinitely many weakly interacting particles with decaying masses, enabling construction of full-dimensional invariant tori in infinite-dimensional systems with long-range interactions.
Oscillatory Motions in the Restricted 3-body Problem: A functional analytic approach , note =
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Existence of half-entire expansive motions with prescribed initial data and asymptotics is shown for homogeneous N-body problems over a wide range of α, together with refined asymptotic expansions and a geometric interpretation via Jacobi-Maupertuis metrics.
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Kolmogorov invariant torus theorem for weakly interacting particles I: Full dimensional tori
An abstract KAM theorem is developed for infinitely many weakly interacting particles with decaying masses, enabling construction of full-dimensional invariant tori in infinite-dimensional systems with long-range interactions.
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Expansive solutions and the boundary at infinity for the homogeneous $N$-body problem
Existence of half-entire expansive motions with prescribed initial data and asymptotics is shown for homogeneous N-body problems over a wide range of α, together with refined asymptotic expansions and a geometric interpretation via Jacobi-Maupertuis metrics.