Sufficient conditions for a map having nonwandering critical points to be Ω-stable are introduced. It is not known if these conditions are necessary, but they are easily verified for all known examples of Ω-stable maps. Their necessity is shown in dimension two. Examples are given of Axiom A maps that have no cycles but are not Ω-stable.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-1-3,
author = {J. Delgado and N. Romero and A. Rovella and F. Vilamaj\'o},
title = {$\Omega$-stability for maps with nonwandering critical points},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {23-35},
zbl = {1114.37017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-1-3}
}
J. Delgado; N. Romero; A. Rovella; F. Vilamajó. Ω-stability for maps with nonwandering critical points. Fundamenta Mathematicae, Tome 193 (2007) pp. 23-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-1-3/