We calculate and study the Lyapunov spectrum of a granular gas maintained i
n a steady state by an isokinetic thermostat. Considering restitution coeff
icients greater than unity allows us to show that the spectra change smooth
ly and continuously at equilibrium. The shearing instability of the granula
r gas, however, provokes an abrupt change in the structure of the spectrum.
The relationship between various physically relevant quantities and the en
ergy dissipation rate differs from previously studied nonequilibrium steady
states.