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arXiv · 1401.6659

The Dynamical Mordell-Lang problem

Jason P. Bell·Dragos Ghioca·Thomas J. Tucker
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Abstract

Let X be a Noetherian space, let f be a continuous self-map on X, let Y be a closed subset of X, and let x be a point on X. We show that the set S consisting of all nonnegative integers n such that f^n(x) is in Y is a union of at most finitely many arithmetic progressions along with a set of Banach density zero. In particular, we obtain that given any quasi-projective variety X, any rational self-map map f on X, any subvariety Y of X, and any point x in X whose orbit under f is in the domain of definition for f, the set S is a finite union of arithmetic progressions together with a set of Banach density zero. We prove a similar result for the backward orbit of a point.

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Jason P. Bell, Dragos Ghioca, Thomas J. Tucker. 2014-01-26. The Dynamical Mordell-Lang problem. https://arxiv.org/abs/1401.6659

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