An exercise in experimental mathematics: calculation of the algebraic entropy of a map

TL;DR

This paper demonstrates how derived recurrences can be used to evaluate the algebraic entropy of self-maps of projective spaces, exemplifying experimental mathematics with a partially proven but highly consistent result.

Contribution

It introduces the application of derived recurrences to compute algebraic entropy, showcasing an experimental approach in algebraic dynamics.

Findings

Consistent results from multiple approaches support the computed algebraic entropy.

The paper provides an instructive example of experimental mathematics in algebraic geometry.

A complete proof for the example remains to be established.

Abstract

We illustrate the use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces. We in particular give an example, where a complete proof is still awaited, but where different approaches are in such perfect agreement that we can trust we get to an exact result. This is an instructive example of experimental mathematics.