Abstract
We numerically evaluate the Lyapunov exponents for the three-dimensional periodic Lorentz gas in an electric field, with a Gaussian thermostat. For small values of the field, the dynamics appears to be ergodic. For larger fields there are chaotic and periodic windows. The Lyapunov exponents are found to obey the conjugate pairing rule in both chaotic and stable regions, indicating that conjugate pairing can occur for small systems, and is not restricted to the large N limit.
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