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 Map## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Nonwandering." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Nonwandering.html