Symmetry reduction and superintegrable Hamiltonian systems

TL;DR

This paper demonstrates how to construct invariant integrals of motion for certain Hamiltonian systems via reduction, establishing their maximal superintegrability and exploring potential generalizations of the method.

Contribution

It introduces a reduction-based method to prove maximal superintegrability and constructs complete sets of integrals for specific Hamiltonian systems.

Findings

Systems are proven to be maximally superintegrable.

Complete sets of invariants are constructed.

Reduction method's potential for generalization is discussed.

Abstract

We construct complete sets of invariant quantities that are integrals of motion for two Hamiltonian systems obtained through a reduction procedure, thus proving that these systems are maximally superintegrable. We also discuss the reduction method used in this article and its possible generalization to other maximally superintegrable systems.