Hyperhamiltonian dynamics

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.

24 pages; to appear in J. Phys. A

References in corpus (3)

• Flows on quaternionic-Kaehler and very special real manifolds
• Quaternionic Hamilton equations
• Quaternionic integrable systems

Cited by in corpus (13)

• Quaternions in mathematical physics (1): Alphabetical bibliography
• Symmetries of the Dirac operators associated with covariantly constant Killing-Yano tensors
• A variational principle for volume-preserving dynamics
• Quaternionic integrable systems
• Geometrical modification of quaternionic quantum mechanics
• Superalgebras of Dirac operators on manifolds with special Killing-Yano tensors
• Structure preserving transformations in hyperkahler Euclidean spaces
• Canonical transformations for hyperkahler structures and hyperhamiltonian dynamics
• Symmetry and quaternionic integrable systems
• Maximal degree variational principles
• Variational principles for involutive systems of vector fields
• Hyper-Hamiltonian quantum mechanics
• Volume preserving bi-Lipschitz homeomorphisms on the Heisenberg group