We give here the first examples of C¹ structurally stable maps on manifolds of dimension greater than two that are neither diffeomorphisms nor expanding. It is shown that an Axiom A endomorphism all of whose basic pieces are expanding or attracting is C¹ stable. A necessary condition for the existence of such examples is also given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm208-1-2,
author = {J. Iglesias and A. Portela and A. Rovella},
title = {C$^1$ stable maps: examples without saddles},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {23-33},
zbl = {1196.37052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm208-1-2}
}
J. Iglesias; A. Portela; A. Rovella. C¹ stable maps: examples without saddles. Fundamenta Mathematicae, Tome 209 (2010) pp. 23-33. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm208-1-2/