Degree Growth of Rational Maps Induced from Algebraic Structures

TL;DR

This paper investigates how the degrees of rational maps, derived from algebraic structures on finite dimensional vector spaces, grow over iterations, providing insights into their dynamical complexity.

Contribution

It characterizes the degree growth of rational maps induced by algebraic structures on finite dimensional vector spaces, a novel connection between algebra and dynamical systems.

Findings

Degree sequences exhibit specific growth patterns.

Established bounds for degree growth rates.

Linked algebraic properties to dynamical complexity.

Abstract

For a finite dimensional vector space equipped with a $\mathbb C$-algebra structure, one can define rational maps using the algebraic structure. In this paper, we describe the growth of the degree sequences for this type of rational maps.