Cocycles, Compatibility, and Poisson Brackets for Complex Fluids

Cendra, H., J. E. Marsden, and T. S. Ratiu

Adv. in Mult. Theories of Con. with Sub., 51-73

Abstract:

Motivated by Poisson structures for complex fluids containing cocycles, such as the Poisson structure for spin glasses given by Holm and Kupershmidt in 1988, we investigate a general construction of Poisson brackets with cocycles. Connections with the construction of compatible brackets found in the theory of integrable systems are also briefly discussed.