Field driven thermostated systems: A nonlinear multibaker map

In this paper we discuss a simple deterministic model for a field driven, thermostated random walk that is constructed by a suitable generalization of a multibaker map. The map is a usual multibaker, but perturbed by a thermostated external field that has many of the properties of the fields used in systems with Gaussian thermostats. For small values of the driving field, the map is hyperbolic and has a unique Sinai-Ruelle-Bowen measure that we determine analytically to first order in the field parameter. We then compute the positive and negative Lyapunov exponents to second order and discuss their relation to the transport properties. For higher values of the parameter, this system becomes nonhyperbolic and possesses an attractive fixed point.