We review the concept of topological recurrence for weak Feller Markov chains on compact state spaces and explore the implications of this concept for the ergodicity of the processes. We also prove some conditions for existence and uniqueness of invariant measures of certain types. Examples are given from the class of iterated function systems on the real line.
"Some Notes on Topological Recurrence." Electron. Commun. Probab. 10 82 - 93, 2005. https://doi.org/10.1214/ECP.v10-1137