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 .
Nonwandering
See also
Anosov Diffeomorphism, Axiom A Diffeomorphism, Smale Horseshoe MapExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Nonwandering." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Nonwandering.html