When the Morse index is infinite

Details When the Morse index is infinite When the Morse index is infinite

2004-03-31

arxiv.org/abs/math/0403552v1

International Mathematics Research Notices 71 (2004) 3839-3854

Mathematics

Dynamical Systems

10 pages

Scientific paper

Let f be a smooth Morse function on an infinite dimensional separable Hilbert manifold, all of whose critical points have infinite Morse index and co-index. For any critical point x choose an integer a(x) arbitrarily. Then there exists a Riemannian structure on M such that the corresponding gradient flow of f has the following property: for any pair of critical points x,y, the unstable manifold of x and the stable manifold of y have a transverse intersection of dimension a(x)-a(y).

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