Field driven thermostated systems: A nonlinear multibaker map

In this paper we discuss a simple deterministic model for a field driven, t hermostated random walk that is constructed by a suitable generalization of a multibaker map. The map is a usual multibaker, but perturbed by a thermo stated 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 d etermine analytically to first order in the field parameter. We then comput e the positive and negative Lyapunov exponents to second order and discuss their relation to the transport properties. For higher values of the parame ter, this system becomes nonhyperbolic and possesses an attractive fixed po int. [S1063-651X(99)03801-5].