Quaternionic integrable systems

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.

10 pages. To appear in the proceedings of the SPT2002 conference, edited by S. Abenda, G. Gaeta and S. Walcher, World Scientific

References in corpus (2)

• Hyperhamiltonian dynamics
• Quaternionic Hamilton equations

Cited by in corpus (6)

• Hyperhamiltonian dynamics
• Quaternions in mathematical physics (1): Alphabetical bibliography
• A variational principle for volume-preserving dynamics
• Canonical transformations for hyperkahler structures and hyperhamiltonian dynamics
• Symmetry and quaternionic integrable systems
• Structure preserving transformations in hyperkahler Euclidean spaces