Recurrence and the asymptotic pseudo-orbit tracing property
The paper introduces the asymptotic pseudo-orbit tracing property (APOTP) for continuous maps from a compact metric space into itself and gives several sufficient and necessary conditions. At the end of the paper it is proved that a homeomorphism that is chain transitive on its omega-limit set and has the APOTP is a (topologically transitive) nonwandering homeomorphism. Note that finding sufficient conditions for nonwandering homeomorphisms has been an interesting problem in dynamical systems, see e.g. \textit{M. Hurley} [J. Differ. Equations 54, 60--72 (1984; Zbl 0493.58013)].
asymptotic pseudo-orbit tracing property
scientific article; zbMATH DE number 5142223