On the algebraic geometry of polynomial dynamical systems

TL;DR

This paper explores the algebraic geometric structure of polynomial dynamical systems over finite fields, highlighting their applications in various scientific and engineering domains and providing methods to analyze their behavior.

Contribution

It introduces an algebraic geometric framework for analyzing polynomial dynamical systems over finite fields, connecting their structure and dynamics to algebraic geometry tools.

Findings

Algebraic geometry provides a powerful language for understanding these systems.

Structural and dynamic problems can be formulated algebraically.

Applications include modeling biochemical networks and control systems.

Abstract

This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks. It is shown that several problems relating to their structure and dynamics, as well as control theory, can be formulated and solved in the language of algebraic geometry.