Lyapunov Instability for a hard-disk fluid in equilibrium and   nonequilibrium thermostated by deterministic scattering
  We compute the full Lyapunov spectra for a hard-disk fluid under temperature gradient and shear. The system is thermalized by deterministic and time-reversible scattering at the boundary. This thermostating mechanism allows for energy fluctuations around a mean value which is reflected by only two vanishing Lyapunov exponents in equilibrium and nonequilibrium. The Lyapunov exponents are calculated with a recently developed formalism for systems with elastic hard collisions. In a nonequilibrium steady state the average phase space volume is contracted onto a fractal attractor leading to a negative sum of Lyapunov exponents. Since the system is driven inhomogeneously we do not expect the conjugate pairing rule to hold which is confirmed numerically. 
C. Wagner (Center for Nonlinear Phenomena and Complex Systems,   Brussels)