Zariski dense orbits for regular self-maps of split semiabelian varieties in positive characteristic

TL;DR

This paper proves the Zariski dense orbit conjecture for regular self-maps on split semiabelian varieties in positive characteristic, advancing understanding in algebraic dynamics.

Contribution

It establishes the conjecture in positive characteristic for a broad class of algebraic varieties, which was previously unresolved.

Findings

Zariski dense orbits are proven to exist for the specified maps.

The result applies specifically to split semiabelian varieties.

This advances the theory of algebraic dynamics in positive characteristic.

Abstract

We prove the Zariski dense orbit conjecture in positive characteristic for regular self-maps of split semiabelian varieties.