A note on some superintegrable Hamiltonian systems

TL;DR

This paper examines specific superintegrable Hamiltonian systems identified via differential Galois group analysis, clarifies their identities, and derives their Poisson algebras to deepen understanding of their structure.

Contribution

It provides a clearer characterization of certain superintegrable systems and derives their Poisson algebras, advancing the theoretical understanding of these systems.

Findings

Identification of specific superintegrable systems

Derivation of their Poisson algebras

Clarification of system identities

Abstract

We consider some examples of superintegrable system which were recently isolated through a differential Galois group analysis. The identity of these systems is clarified and the corresponding Poisson algebras derived.