The term "positive recurrence" refers to a situation in which a state of a system will be visited repeatedly over time. However, there are several synonyms you can use to describe this phenomenon. For example, you might use the term "ergodicity" to describe a system that is visited repeatedly and has a stationary, time-independent distribution of states. Alternatively, you could use the term "repetitive transient" to describe a situation in which a system returns to a state many times before eventually leaving it. Other synonyms that may be used include "cyclic behavior", "persistent state", and "periodic recurrence". Each of these terms conveys a slightly different aspect of the same underlying phenomenon of repeated system states.