On the global stable manifold

Details On the global stable manifold On the global stable manifold

2005-06-15

arxiv.org/abs/math/0506292v2

Studia Math. 177 (2006), 113-131.

Mathematics

Dynamical Systems

18 pages, LaTeX2e file. Revised version (corrected typos, introduction slightly extended). To appear in Studia Mathematica

Scientific paper

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 diffeomorphism class of the global stable manifold, a problem
which in the general Banach setting gives rise to subtle questions about the
possibility of extending germs of diffeomorphisms.

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