  Let $f:X\rightarrow X$ be a quasi-finite endomorphism of an algebraic variety
$X$ defined over a number field $K$ and fix an initial point $a\in X$. We
consider a special case of the dynamical Mordell-Lang Conjecture, where the
subvariety $V$ contains only finitely many periodic points and does not contain
any positive-dimensional periodic subvariety. We show that the set $\{n\in
\mathbb{N}~|~f^n(a) \in V \}$ satisfies a strong gap principle.
