Fast dynamo action on the 3-torus for pulsed-diffusions

For the passive vector equation, the fast dynamo conjecture predicts exponential-in-time growth of the L^2 norm of the solution under a Lipschitz flow of a vector field, at a rate independent of the resistivity. We establish this conjecture for the pulsed diffusion model with a time-periodic stretch-fold-shear (SFS) vector field. Our approach uses anisotropic Banach spaces adapted to the dynamics of the underlying flow to establish the existence of a distributional eigenfunction associated with a discrete eigenvalue of modulus greater than one in the zero diffusivity case and treating the resistive effect as a perturbation in this anisotropic Banach spaces.