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math.DS2005★ 1 cited
On the global stable manifold
Alberto Abbondandolo, Pietro Majer
We give an alternative proof of the stable manifold theorem as an application of the (right and left) inverse mapping theorem on a space of sequences. We investigate the diffeomorp…
math.DS2004
When the Morse index is infinite
Alberto Abbondandolo, Pietro Majer
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…
math.DS2003★ 45 cited
A Morse complex for infinite dimensional manifolds - Part I
Alberto Abbondandolo, Pietro Majer
In this paper and in the forthcoming Part II we introduce a Morse complex for a class of functions f defined on an infinite dimensional Hilbert manifold M, possibly having critical…