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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-2,
author = {Alberto Abbondandolo and Pietro Majer},
title = {On the global stable manifold},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {113-131},
zbl = {1105.37018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-2}
}
Alberto Abbondandolo; Pietro Majer. On the global stable manifold. Studia Mathematica, Tome 173 (2006) pp. 113-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-2/