Axiom A systems

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 $f\ .$