Zariski dense orbits for endomorphisms of a power of the additive group scheme defined over finite fields

TL;DR

This paper proves the Zariski dense orbit conjecture for endomorphisms of powers of the additive group over algebraically closed finite fields, advancing understanding in algebraic dynamics in positive characteristic.

Contribution

It establishes the conjecture in positive characteristic for a broad class of endomorphisms of additive groups over finite fields.

Findings

Zariski dense orbit conjecture proven in positive characteristic

Applicable to endomorphisms of b^N over ar{\u211d}_p

Enhances understanding of algebraic dynamics in finite field settings

Abstract

We prove the Zariski dense orbit conjecture in positive characteristic for endomorphisms of $\mathbb{G}_a^N$ defined over $\overline{\mathbb{F}_p}$.