Axiom A maps are dense in the space of unimodal maps in the \(C^k\) topology. (English) Zbl 1215.37022

Kozlovski, O. S.

Ann. Math. (2) 157, No. 1, 1-43 (2003).

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

MSC:

37D20	Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37C20	Generic properties, structural stability of dynamical systems
37D05	Dynamical systems with hyperbolic orbits and sets
37F10	Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets