When the Morse index is infinite

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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).
10 pages

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Dynamical Systems, Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/70668

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0403552
 http://arxiv.org/abs/math/0403552
 International Mathematics Research Notices 71 (2004) 3839-3854

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arXiv