What's the most specific name for a collection of directed graphs (possibly cyclic) that maps the orbit of a function?
Can't be a forest or a polyforest because cycles not allowed in trees. But the correct term isn't jumping out at me.
An example: the graph of the orbit of $x\mapsto p^{-1}\cdot(x-(x\pmod p))$ through the $p-$adic integers.
(Here $x\pmod p$ is the function that maps to the natural number $n$ representative of some element of $\Bbb Z/p\Bbb Z$ which is $0\leq n<p$)
This "forest" has uncountably many connected graphs, many cyclic. The cyclic graphs of period $m$ are enumerated and classified by the base $p$ Lyndon words of length $m$.