# Axiom A systems

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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 $$f\ .$$