TL;DR
This paper introduces a new solvable many-body goldfish-type model, explores its isochronous variant, and investigates its equilibrium behavior, leading to notable Diophantine results and conjectures.
Contribution
It presents a novel solvable model of goldfish type and analyzes its isochronous variant, connecting different approaches to solvable dynamical systems.
Findings
Identification of a new solvable many-body goldfish-type model
Discovery of an isochronous variant with unique properties
Derivation of a Diophantine result and related conjectures
Abstract
A new solvable many-body problem of goldfish type is identified and used to revisit the connection among two different approaches to solvable dynamical systems. An isochronous variant of this model is identified and investigated. Alternative versions of these models are presented. The behavior of the alternative isochronous model near its equilibrium configurations is investigated, and a remarkable Diophantine result, as well as related Diophantine conjectures, are thereby obtained.
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