Nonhyperbolic behavior in the thermostated Lorentz gas

We show that nonhyperbolic behavior in the length-2 periodic orbits of the thermostated random Lorentz gas occurs only at field strengths greater than unity. For the thermostatted periodic Lorentz gas the range of fields is reduced further due to pruning. Stability analysis shows that there are three classes of period-2 orbits: elliptic orbits and two different hyperbolic orbits. Within the nonergodic elliptic region, trajectories manifest complex behavior that resembles that of perturbed resonant tori in Hamiltonian systems. We present a detailed dynamical study of the nonhyperbolic region.