Kinematic Fast Dynamo Problems

Stars and planets possess magnetic fields that permanently change. Earth, for instance, mysteriously interchanges its north and south magnetic poles, so that the time pattern of the switches forms a Cantor-type set on the time scale (see [AnS]). The mechanism of generation of magnetic fields in astrophysical objects (or in electrically conducting fluids) constitutes the subject of dynamo theory. Kinematic dynamo theory studies what kind of fluid motion can induce exponential growth of a magnetic field for small magnetic diffusivity. Avoiding analytical and numerical results (though crucial for this field), we address below the topological side of the theory.