Fractals and dynamical chaos in a two-dimensional Lorentz gas with sinks

We consider a two-dimensional periodic reactive Lorentz gas, in which a moving point particle undergoes elastic collisions on fixed hard disks and annihilates on absorbing disks, called sinks. We present clear evidence of the existence of a fractal repeller in this open system. Moreover, we establish a relation between the reaction rate, describing the macroscopic evolution of the system, and two characteristic quantities of the microscopic chaos: the average Lyapunov exponent and the Hausdorff codimension of the fractal repeller.