Persistence of order and structure in chaos (Q1081174)

Let \(f\in C^{1+\alpha}(X,X)\) be a nonsingular axiom A mapping from an interval X into itself. There is a positive integer p such that almost every point x in X is asymptotically periodic with period p, provided that f(X) is bounded. This asymptotically periodic behavior is persistent under small smooth perturbations. The topological structure of the nonwandering set of f is described also. It is proved that this structure is invariant under small \(C^ 1\) perturbations of f.