Near a non-degenerate orbit of Stokes waves over a flat bottom, any small periodic bottom perturbation gives rise to at least two distinct steady water waves.
Braids of the N-body problem by cabling a body in a central configuration
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abstract
We prove the existence of periodic solutions of the N=(n+1)-body problem starting with n bodies whose reduced motion is close to a non-degenerate central configuration and replacing one of them by the center of mass of a pair of bodies rotating uniformly. When the motion takes place in the standard Euclidean plane, these solutions are a special type of braid solutions obtained numerically by C. Moore. The proof uses blow-up techniques to separate the problem into the n-body problem, the Kepler problem, and a coupling which is small if the distance of the pair is small. The formulation is variational and the result is obtained by applying a Lyapunov-Schmidt reduction and by using the equivariant Lyusternik-Schnirelmann category.
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Steady waves in flows over periodic bottoms
Near a non-degenerate orbit of Stokes waves over a flat bottom, any small periodic bottom perturbation gives rise to at least two distinct steady water waves.