The nonlinear dynamo problem: Small oscillatory solutions in a strongly simplified model

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Abstract
For a dynamo model obtained by idealizing features of the Sun, an analytic proof of the existence and a recursion formula for the determination of small time periodic solutions in a finite vicinity of the critical dynamo numbers are given. The nonlinear problem is solved by transforming the boundary value problem of the induction equation into a fixed point problem in an infinite dimensional sequence space and then applying the LYAPUNOV‐SCHMIDTmethod to reduce it to a relationship between dynamo number, amplitude and frequency.