A new concept of stability, closely related to that of structural stability, is introduced and applied to the study of C¹ endomorphisms with singularities. A map that is stable in this sense is conjugate to each perturbation that is equivalent to it in a geometric sense. It is shown that this kind of stability implies Axiom A and Ω-stability, and that every critical point is wandering. A partial converse is also shown, providing new examples of C³ structurally stable maps.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-5,
author = {J. Iglesias and A. Portela and A. Rovella},
title = {Stability modulo singular sets},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {155-175},
zbl = {1179.37029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-5}
}
J. Iglesias; A. Portela; A. Rovella. Stability modulo singular sets. Fundamenta Mathematicae, Tome 205 (2009) pp. 155-175. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-5/