Autocatalytic reactions in systems with hyperbolic mixing: exact results for the active Baker map

We investigate the effects of hyperbolic hydrodynamical mixing on the react ion kinetics of autocatalytic systems. Exact results are derived for the tw o-dimensional open Baker map as an underlying mixing dynamics for a two-com ponent autocatalytic system, A+B --> 2B, We prove that chaotic advection mo delled by the Baker map enhances the productivity of the reaction which is due to the fact that the reaction kinetics is catalysed by the fractal unst able manifold of the chaotic set of the reaction-free dynamics. The results are compared with phenomenological theories of active advection.