Giovanni Gallavotti, Lamberto Rondoni, Enrico Segre
Lyapunov spectra and nonequilibrium ensembles equivalence in 2D fluid mechanics
(91K, latex, with 13 postcript figures. gzipped tar package)

ABSTRACT.  We perform numerical experiments to study the Lyapunov spectra of 
dynamical systems associated with the Navier--Stokes (NS) equation in 
two spatial dimensions truncated over the Fourier basis. Recently new 
equations, called GNS equations, have been introduced and conjectured 
to be equivalent to the NS equations at large Reynolds numbers. The 
Lyapunov spectra of the NS and of the corresponding GNS systems 
overlap, adding evidence in favor of the conjectured equivalence 
already studied and partially extended in previous papers. We make 
use of the Lyapunov spectra to study a fluctuation relation which had been proposed to extend the ``fluctuation theorem'' to strongly dissipative systems. Preliminary results towards the formulation of a local version of the fluctuation formula are also presented.