Suppose the orbit of a function $f:X\to X$ only surjects over $Y\subsetneq X$ then $X\setminus Y$ is not in the range of $f$.
These elements $X\setminus Y$ are the leaves of the graph of $f$'s orbit in $X$.
Is there a terminology for this set $X\setminus Y$ as a component of $f$'s orbit or action?
We have that $f$ surjects over $Y$ or may be an epimorphism but is there a phrase for the preimage of the orbit that is not in the image?