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.

• 14H70 - Relationships between algebraic curves and integrable systems
• 34M55 - Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
• 37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
• 37J35 - Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
• 39A36 - Integrable difference and lattice equations; integrability tests
• 54C70 - Entropy in general topology