# On intersections of polynomial semigroups orbits with plane lines

## TL;DR

This paper investigates how orbits generated by polynomial semigroups intersect with lines in the affine plane over a number field, extending prior research in the field.

## Contribution

It extends previous work by analyzing the intersections of polynomial semigroup orbits with lines over number fields, providing new insights into their structure.

## Key findings

- Characterization of orbit-line intersections over number fields
- Extension of previous results to broader classes of polynomial semigroups
- New criteria for when orbits intersect lines in the affine plane

## Abstract

We study intersections of orbits in polynomial semigroup dynamics with lines on the affine plane over a number field, extending previous work of D. Ghioca, T. Tucker, M. Zieve (2008)