A point in a Manifold is said to be nonwandering if, for every open Neighborhood of , it is true that for a Map for some . In other words, every point close to has some iterate under which is also close to . The set of all nonwandering points is denoted , which is known as the nonwandering set of .
See also Anosov Diffeomorphism, Axiom A Diffeomorphism, Smale Horseshoe Map