# Algebraic entropy of a class of five-point differential-difference equations

## TL;DR

This paper calculates the algebraic entropy of certain five-point differential-difference equations, confirming their integrability by showing they have zero entropy, consistent with previous symmetry-based classifications.

## Contribution

It provides a systematic computation of algebraic entropy for a class of integrable equations, validating the classification with an entropy-based approach.

## Key findings

- All equations in the class have vanishing algebraic entropy.
- Algebraic entropy results agree with the generalized symmetry method.
- The method confirms integrability of the classified equations.

## Abstract

We compute the algebraic entropy of a class of integrable Volterra-like five-point differential-difference equations recently classified using the generalised symmetry method. We show that, when applicable, the results of the algebraic entropy agrees with the result of the generalised symmetry method, as all the equations in this class have vanishing entropy.