# Axiom A systems

From Scholarpedia

Dr. Steve Smale, Toyota Technological Institute at Chicago, IL, was invited on 27 October 2010.

Suppose \(f\) is a diffeomorphism of a compact manifold \(M\ .\) \(f\) satisfies Smale's Axiom A if the set of nonwandering points of \(f\) is hyperbolic and equal to the closure of the periodic points of \(f\ .\)