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A Gap Principle for Subvarieties with Finitely Many Periodic Points

Part of: Arithmetic and non-Archimedean dynamical systems Algebraic number theory: local and $p$-adic fields

Published online by Cambridge University Press:  28 February 2020

Keping Huang
Keping Huang*
Affiliation:
Department of Mathematics, University of Rochester, Rochester, NY 14627, USA Email: keping.huang@rochester.edu
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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 $\{n\in \mathbb{Z}_{{\geqslant}0}\mid f^{n}(a)\in V\}$ satisfies a strong gap principle.

Keywords

dynamical Mordell-Lang conjecturegap principle

MSC classification

Primary: 37P05: Polynomial and rational maps
Secondary: 37P55: Arithmetic dynamics on general algebraic varieties 11S82: Non-Archimedean dynamical systems 37P35: Arithmetic properties of periodic points
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 2 , June 2020 , pp. 382 - 392
Copyright
© Canadian Mathematical Society 2019

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