Kinematic fast dynamo problem

In the present work we develop an approach to the classical kinematic fast dynamo problem for flows [32] in the real 3-dimensional space. We suggest a fluid flow that may possibly generate a magnetic field which energy grows exponentially fast with time in the present of slow diffusivity. In order to verify the construction we study a discrete system and prove that an analogous statement holds true for the Poincaré map of the provisional flow and vector fields in the plane. This problem falls into the framework of open dynamical systems with random holes