Bounding periods of subvarieties of (P^1)^n

TL;DR

This paper establishes bounds on the orbit length of periodic subvarieties in (P^1)^n using p-adic analysis and Medvedev-Scanlon's classification, advancing understanding of dynamical systems in algebraic geometry.

Contribution

It introduces a method combining p-adic analysis with existing classification results to bound orbit lengths of periodic subvarieties.

Findings

Bounded the orbit length of periodic subvarieties

Applied p-adic analysis techniques

Extended previous classification results

Abstract

Using methods of p-adic analysis, along with the powerful result of Medvedev-Scanlon (Annals of Mathematics, 2014) for the classification of periodic subvarieties of (P^1)^n, we bound the length of the orbit of a periodic subvariety Y of (P^1)^n under the action of a dominant endomorphism.