On the algebraic structure of rational discrete dynamical systems

TL;DR

This paper explores how singularities influence the evolution of rational discrete dynamical systems, revealing algebraic structures that enable exact entropy calculations and polynomial factorizations, supported by diverse examples.

Contribution

It introduces a framework linking singularities to algebraic properties of rational discrete systems, including generalized Hirota forms and entropy evaluation.

Findings

Singularities determine the evolution patterns of the systems.

Explicit examples demonstrate the theoretical concepts.

Polynomial factorization properties are characterized and utilized.

Abstract

We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other things generalised Hirota form, exact evaluation of the algebraic entropy as well as remarkable polynomial factorisation properties. We illustrate the phenomenon explicitly with examples covering a wide range of models.