TL;DR
This paper introduces hyperhamiltonian dynamics, an extension of Hamiltonian systems on hyperkähler manifolds, highlighting its features and exploring quaternionic oscillators as examples of integrable hyperhamiltonian systems.
Contribution
It presents the concept of hyperhamiltonian dynamics on hyperkähler manifolds and analyzes quaternionic oscillators as prototypical integrable systems.
Findings
Hyperhamiltonian dynamics shares features with standard Hamiltonian systems.
Quaternionic oscillators serve as examples of integrable hyperhamiltonian systems.
The framework extends Hamiltonian mechanics to hyperkähler geometry.
Abstract
We introduce an extension of hamiltonian dynamics, defined on hyperkahler manifolds, which we call ``hyperhamiltonian dynamics''. We show that this has many of the attractive features of standard hamiltonian dynamics. We also discuss the prototypical integrable hyperhamiltonian systems, i.e. quaternionic oscillators.
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