Recent results for the thermostatted Lorentz gas

We review the behaviour of a driven, thermostatted Lorentz gas. The two variable Poincaré section confirms that the “attractor” fills the whole phase space, and that the associated stationary measure is ergodic and multifractal for fields below 2.2. Such a property of the “attractor” ends with either a crisis or the emergence of elliptical regions, followed eventually by stable orbits. We present, accurate periodic orbit expansion calculations for the diffusion coefficient, pressure and Lyapunov exponent. The periodic orbit approach suggests the definition of a partition function and gives a simple explanation for a positive conductivity and diffusion coefficient.