$\Omega $-stability for maps with nonwandering critical points
Volume 193 / 2007
Fundamenta Mathematicae 193 (2007), 23-35
MSC: Primary 37D20.
DOI: 10.4064/fm193-1-3
Abstract
Sufficient conditions for a map having nonwandering critical points to be ${\mit\Omega} $-stable are introduced. It is not known if these conditions are necessary, but they are easily verified for all known examples of ${\mit\Omega} $-stable maps. Their necessity is shown in dimension two. Examples are given of Axiom~A maps that have no cycles but are not ${\mit\Omega} $-stable.
