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arXiv · 1808.02849

A Gap Principle for Subvarieties with Finitely Many Periodic Points

Keping Huang
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Abstract

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.

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Keping Huang. 2018-08-08. A Gap Principle for Subvarieties with Finitely Many Periodic Points. https://doi.org/10.4153/s0008439519000481

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