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