Generic Homeomorphisms have the Pseudo-Orbit Tracing Property
Kenzi Odani · Proceedings of the American Mathematical Society · 1990
Let $M(\operatorname {dim} M \leq 3)$ be a compact manifold. Then a generic $f \in \operatorname {Homeo}(M)$ satisfies the following: $f$ has the pseudo-orbit tracing property; $f$ is ${C^0}$ tolerance stable; and $f$ is not topologically stable.