Metriplectic Systems

Daniel Fish

ABSTRACT
A metriplectic structure on a smooth manifold M is a pair of coemiant tensors P and g, which are skew-symmetric and symmetric respectively. A metriplectic system is a dynamical system defined by the equations dx/dt=PdH+gdS for smooth functions H and S on M. We investigate the geometric aspects of metriplectic dynamical systems on smooth manifolds equipped with metriplectic structures. We discuss several topics related to metriplectic systems, including linear connections which preserve P and g, representations of known dynamical systems as metriplectic systems, metriplectic dynamics on Lie algebras, generalized Harmonic systems, and geometric perturbations of Hamiltonian systems.

May 13, 2005
DISSERTATION COMMITTEE
Serge Preston, Chairman
Steven Bleiler
Andrew M. Fraser
Peter Veerman
Pui-Tak Leung, Graduate Studies Rep.