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

TL;DR

This paper proves a dynamical version of the Mordell-Lang conjecture for subvarieties under a morphism, using nonarchimedean dynamics and analytic methods to advance understanding of periodic points and linearization.

Contribution

It introduces a dynamical Mordell-Lang theorem for quasiprojective varieties with new analytic techniques based on nonarchimedean dynamics.

Findings

Establishes a dynamical Mordell-Lang conjecture in new settings

Develops an analytic approach combining Skolem, Mahler, Lech techniques with Herman and Yoccoz results

Provides insights into periodic points and linearization in dynamical systems

Abstract

We prove a dynamical version of the Mordell-Lang conjecture for subvarieties of quasiprojective varieties X, endowed with the action of a morphism f:X --> X. We use an analytic method based on the technique of Skolem, Mahler, and Lech, along with results of Herman and Yoccoz from nonarchimedean dynamics.