Nonwandering

Abstract

Consider a dynamical system given by a locally compact metric space X and a continuous map T: X → X. A point in X is wandering if it admits a neighborhood that is disjoint from all of its iterates.

With many a weary step, and many a groan,

Up the high hill he heaves a huge round stone;

The huge round stone, resulting with a bound,

Thunders impetuous down, and smokes along the ground.

Again the restless orb his toil renews,

Dust mounts in clouds, and sweat descends in dews.

Homer