$C^1$-maps having hyperbolic periodic points
Fundamenta Mathematicae 169 (2001), 1-49 MSC: Primary 37C20, 37D20, 34D30. DOI: 10.4064/fm169-1-1
We show that the $C^1$-interior of the set of maps satisfying the following conditions:
(i) periodic points are hyperbolic,(ii) singular points belonging to the nonwandering set are sinks, coincides with the set of Axiom A maps having the no cycle property.