Periodic points, linearizing maps, and the dynamical Mordell–Lang problem

By Dragos Ghioca, T. Tucker. 2008

95 citations recorded by the source corpus.

Under suitable hypotheses, we prove a dynamical version of the Mordell‐Lang conjecture for subvarieties of quasiprojective varieties X, endowed with the action of a morphism ! : X " X. We also prove a version of the Mordell‐Lang conjecture that holds for any endomorphism of a semiabelian variety. We use an analytic method based on the technique of Skolem, Mahler, and Lech, along with results of Herman and Yoccoz from nonarchimedean dynamics.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1ede03a4ee0d588a988f407d22f715451a391f45

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Examples of dynamical degree equals arithmetic degree (2012, unknown): “One might start by citing the Skolem–Lech–Mahler theorem on linear recurrences and Chaubauty’s result on rational points on curves [8], as well as more recent results in arithmetic dynamics, including for example papers on the dynamical Mordell–Lang conjecture [5, 6, 10] and applications to potentia”
Current trends and open problems in arithmetic dynamics (2018, unknown): “1 (Dynamical Mordell–Lang Conjecture: Bell, 2006, [17]; Denis, 1994, [56]; Ghioca–Tucker, 2009, [85]).”
A case of the dynamical Mordell–Lang conjecture (2012, methodology): “In the cases of endomorphisms of semiabelian varieties (see [11,12,15,34]), of automorphisms of affine varieties (see [5,9]), or of étale endomorphisms in general (see [6]), the underlying maps have no ramification.”