Dynamical Mordell-Lang conjecture for birational polynomial morphisms on $\mathbb{A}^2$

TL;DR

This paper proves the dynamical Mordell-Lang conjecture for a specific class of polynomial morphisms on the affine plane, advancing understanding in algebraic dynamics.

Contribution

It establishes the conjecture for birational polynomial morphisms on , a case previously unresolved in the field.

Findings

Confirmed the conjecture for birational polynomial morphisms on 

Provided new techniques for analyzing polynomial dynamical systems

Enhanced understanding of orbit intersections in algebraic geometry

Abstract

We prove the dynamical Mordell-Lang conjecture for birational polynomial morphisms on $\mathbb{A}^2$.