Algebraic entropy for systems of quad equations

TL;DR

This paper explores the calculation of algebraic entropy for systems of quad equations, highlighting the need to restrict evolution directions in cases with algebraic solutions, and discusses examples from existing literature.

Contribution

It introduces a framework for calculating algebraic entropy in systems of quad equations, especially when solutions are algebraic, and discusses relevant examples.

Findings

Algebraic entropy can be computed for systems of quad equations.

Restrictions on evolution directions are sometimes necessary due to algebraic solutions.

Examples from literature illustrate the proposed framework.

Abstract

In this work I discuss briefly the calculation of the algebraic entropy for systems of quad equations. In particular, I observe that since systems of multilinear equations can have algebraic solution, in some cases one might need to restrict the direction of evolution only to the pair of vertices yielding a birational evolution. Some examples from the exiting literature are presented and discussed within this framework.