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Published online by Cambridge University Press: 28 February 2020
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
$\{n\in \mathbb{Z}_{{\geqslant}0}\mid f^{n}(a)\in V\}$ satisfies a strong gap principle.