What is This Set Called?

Let S be a finite set, and let f:S-->S be a function. Then consider the
sequence of sets S, f(S), f(f(S)), f(f(f(S))), f(f(f(f(S))))...
Call the intersection of all of these X. X has the interesting property
that it is the largest subset of S on which f is a permutation. Does X
have a name? If so, what is X called?

---- David

To send me email, move the r from the beginning to the end of the part
before the @ and insert "alum." at the beginning of the part after the
@. If you are a spammer and you still foolishly use the email address
with which I post, then HA HA HA. IT SUCKS TO BE YOU, for that account
exists no longer.

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