Abstract
Abstract We study the spectrum of the operator describing the growth of magnetic fields in an infinitely conducting, incompressible fluid. We show that, in many circumstances, it consists of an annulus and also give characterization of this spectrum by the Lyapunov exponents of periodic orbits of the Lagrangian flow. We also consider the effect on the spectrum of considering only spaces of vector fields with zero divergence—a physically reasonable restriction for magnetic fields—and find that, for many systems, even if the outer edges of the spectrum are not changed, there appear non-trivial components of residual spectrum.
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