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A Gap Principle for Subvarieties with Finitely Many Periodic Points
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 63 / Issue 2 / June 2020
- Published online by Cambridge University Press:
- 28 February 2020, pp. 382-392
- Print publication:
- June 2020
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- Article
- Export citation
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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.
