Interesting system of 3 first-order recursions

2024/09/08 by Calogero, Francesco
#Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.2409.05074

Abstract

In this paper we firstly review how to explicitly solve a system of 3 first-order linear recursions and outline the main properties of these solutions. Next, via a change of variables, we identify a class of systems of 3 first-order nonlinear recursions which also are explicitly solvable. These systems might be of interest for practitioners in applied sciences: they allow a complete display of their solutions, which may feature interesting behaviors, for instance be completely periodic ("isochronous systems", if the independent variable n=0,1,2,3...is considered a ticking time), or feature this property only asymptotically (as n→ ∞ ).

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