Carlsson, Niclas Some notes on topological recurrence. (English) Zbl 1108.37008 Electron. Commun. Probab. 10, 82-93 (2005). Summary: 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. MSC: 37B20 Notions of recurrence and recurrent behavior in topological dynamical systems 37A05 Dynamical aspects of measure-preserving transformations 37A25 Ergodicity, mixing, rates of mixing 60J05 Discrete-time Markov processes on general state spaces Keywords:Feller Markov chains; ergodicity; invariant measures; iterated function systems PDFBibTeX XMLCite \textit{N. Carlsson}, Electron. Commun. Probab. 10, 82--93 (2005; Zbl 1108.37008) Full Text: DOI EuDML