  We prove that self-mappings of uniquely arcwise connected locally arcwise
connected spaces are pointwise-recurrent if and only if all their cutpoints are
periodic while all endpoints are either periodic or belong to what we call
"topological weak adding machines". We also introduce the notion of a \emph{ray
complete} uniquely arcwise connected locally arcwise connected space and show
that for them the above "topological weak adding machines" coincide with
classical adding machines (e.g., this holds if the entire space is compact).
