A Gap Principle for Subvarieties with Finitely Many Periodic Points
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AbstractLet $f:X\rightarrow X$ 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.
2012 ◽
Vol 08
(01)
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pp. 175-188
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2011 ◽
Vol 147
(6)
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pp. 1819-1842
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2014 ◽
Vol 36
(3)
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pp. 944-972
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1985 ◽
Vol 5
(3)
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pp. 321-327
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2016 ◽
Vol 12
(08)
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pp. 2201-2229
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2017 ◽
Vol 13
(04)
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pp. 991-1001
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