Quaternionic integrable systems

TL;DR

This paper explores quaternionic generalizations of integrable systems and Hamiltonian dynamics, extending classical concepts related to complex rotations to quaternionic and hyperKahler structures, broadening the scope of integrability.

Contribution

It introduces a novel framework for quaternionic integrable systems and Hamiltonian dynamics based on hyperKahler structures, expanding classical theories beyond complex rotations.

Findings

Quaternionic integrable systems generalize classical integrable systems.

HyperKahler structures enable a broader class of Hamiltonian dynamics.

The framework extends the properties of Arnold-Liouville integrability.

Abstract

Standard (Arnold-Liouville) integrable systems are intimately related to complex rotations. One can define a generalization of these, sharing many of their properties, where complex rotations are replaced by quaternionic ones. Actually this extension is not limited to the integrable case: one can define a generalization of Hamilton dynamics based on hyperKahler structures.