Interesting system of $3$ first-order recursions

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Autore principale:	Calogero, Francesco
Natura:	Preprint
Pubblicazione:	2024
Soggetti:	Exactly Solvable and Integrable Systems Dynamical Systems
Accesso online:	Acceder al recurso
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_version_	1866916386178072576
author	Calogero, Francesco
author_facet	Calogero, Francesco
contents	In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{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 $3$ \textit{first-order nonlinear recursions} which also are \textit{explicitly solvable}. These systems might be of interest for practitioners in \textit{applied} sciences: they allow a complete display of their solutions, which may feature interesting behaviors, for instance be \textit{completely periodic} ("isochronous systems", if the independent variable $n=0,1,2,3...$is considered a \textit{ticking time}), or feature this property \textit{only asymptotically} (as\textit{\ }$n\rightarrow \infty $).
format	Preprint
id	arxiv_https___arxiv_org_abs_2409_05074
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Interesting system of $3$ first-order recursions Calogero, Francesco Exactly Solvable and Integrable Systems Dynamical Systems In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{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 $3$ \textit{first-order nonlinear recursions} which also are \textit{explicitly solvable}. These systems might be of interest for practitioners in \textit{applied} sciences: they allow a complete display of their solutions, which may feature interesting behaviors, for instance be \textit{completely periodic} ("isochronous systems", if the independent variable $n=0,1,2,3...$is considered a \textit{ticking time}), or feature this property \textit{only asymptotically} (as\textit{\ }$n\rightarrow \infty $).
title	Interesting system of $3$ first-order recursions
topic	Exactly Solvable and Integrable Systems Dynamical Systems
url	https://arxiv.org/abs/2409.05074

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