Stability modulo singular sets
Tom 204 / 2009
Fundamenta Mathematicae 204 (2009), 155-175
MSC: Primary 37C20; Secondary 58K05.
DOI: 10.4064/fm204-2-5
Streszczenie
A new concept of stability, closely related to that of structural stability, is introduced and applied to the study of $C^1$ 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 ${\Omega }$-stability, and that every critical point is wandering. A partial converse is also shown, providing new examples of $C^3$ structurally stable maps.
