Axiom A maps are dense in the space of unimodal maps in the $C^k$ topology

Abstract

In this paper we prove $C^k$ structural stability conjecture for unimodal maps. In other words, we shall prove that Axiom A maps are dense in the space of $C^k$ unimodal maps in the $C^k$ topology. Here $k$ can be $1,2,\ldots,\infty,\omega$.