Spiralling invariant manifolds
This paper is concerned with polar coordinate systems on a neighborhood of codimensional 2 submanifolds, and a definition of the concept of a multidimensional spiralling manifold. The author also develops a criterion for when two spirals which spiral in opposite directions must intersect, and then gives a proof that spirals of this type are created when an invariant manifold passes through a neighborhood of a hyperbolic restpoint with complex eigenvalues. When combined with the intersection theory, the results show that spiralling can function as a mechanism for producing intersections of invariant manifolds in high dimensions. Finally, the author exploits this mechanism to prove the existence of infinitely many solutions of the isosceles 3-body problem which experience triple collisions in both forward and backward time.
scientific article; zbMATH DE number 4032653