FAST DYNAMOS AND DETERMINANTS OF SINGULAR INTEGRAL-OPERATORS

The dynamo problem is considered for mappings with pulsed diffusion in the fast dynamo limit of vanishing magnetic diffusion. It is shown ho w the determinant of a dynamo operator may be expanded in terms of sum s over the periodic orbits of the mapping. In mappings for which all t he orbits are hyperbolic the limit of weak diffusion may be taken form ally, yielding a prescription for calculating the fast dynamo growth r ate from information about the periodic orbits. A mathematical justifi cation for taking the limit of weak diffusion has not been obtained. N evertheless it is verified that the prescription for calculating fast dynamo growth rates from periodic orbit sums gives correct growth rate s for a number of models, including stretch-fold-shear and cat maps wi th shear.