Abstract
We demonstrate that in the thermostated three-dimensional Lorentz gas, the symmetry of the Lyapunov spectrum can be broken by adding to the system an external magnetic field not perpendicular to the electric field. For perpendicular field vectors, there is a Hamiltonian reformulation of the dynamics and the conjugate pairing rule still holds. This indicates that symmetric Lyapunov spectra have nothing to do with time-reversal symmetry or reversibility; instead, it seems to be related to the existence of a Hamiltonian connection.
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