Some notes on topological recurrence. (English) Zbl 1108.37008

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.


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
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