Stability modulo singular sets.

The paper studies a new concept, structural stability modulo singular sets, which has been introduced by the authors in [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 6, 1209–1220 (2008; Zbl 1153.37329)]. This concept is applied to the study of C 1 endomorphisms with singularities. From the abstract: “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 C 3 structurally stable maps.”