Denis V. Juriev
Symmetric Designs on Lie Algebras and Interactions of Hamiltonian Systems
Preprint series: ESI preprints

MSC:

58F05 Hamiltonian and Lagrangian systems; symplectic geometry, See also {70Hxx, 81S10}

17B81 Applications to physics

Abstract: Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical
equations are constructed by use of symmetric designs on Lie algebras.
The results of analysis of these equations show that some class of
symmetric designs on Lie algebras beyond Jordan ones may be useful for a
description of almost periodic, asymptotically periodic, almost asymptotically
periodic, and possibly, more chaotic systems. However, the behaviour of
systems related to symmetric designs with additional identities is simpler
than for general ones from different points of view. These facts confirm a
general thesis that various algebraic structures beyond Lie algebras may be
regarded as certain characteristics for a wide class of dynamical systems.

Keywords: Classical dynamics, Lie algebras, hamiltonian systems, nonhamiltonian interaction, triple systems