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The spectrum of the spherically symmetric alpha-2 dynamo is studied in thecase of idealized boundary conditions. Starting from the exact analyticalsolutions of models with constant alpha-profiles a perturbation theory and aGalerkin technique are developed in a Krein-space approach. With the help ofthese tools a very pronounced alpha-resonance pattern is found in thedeformations of the spectral mesh as well as in the unfolding of the diabolicalpoints located at the nodes of this mesh. Non-oscillatory as well asoscillatory dynamo regimes are obtained. A Fourier component based estimationtechnique is developed for obtaining the critical alpha-profiles at which theeigenvalues enter the right spectral half-plane with non-vanishing imaginarycomponents (at which overcritical oscillatory dynamo regimes form). Finally,Frechet derivative (gradient) based methods are developed, suitable for furthernumerical investigations of Krein-space related setups like MHD alpha-2-dynamosor models of PT-symmetric quantum mechanics.Comment: 22 pages, 7 figures, presented at the 4th International Workshop on  Pseudo-Hermitian Hamiltonians in Quantum Physics, November 23-25, 2005,  Stellenbosch, South Africa; minor typos corrected, refs adde

A Krein space related perturbation theory for MHD α2-dynamos and resonant unfolding of diabolical points

A Krein space related perturbation theory for MHD α²-dynamos and resonant unfolding of diabolical points