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Critical exponents are calculated exactly at the onset of an instability,using asymptotic expansiontechniques. When the unstable mode is subject tomultiplicative noise whose spectrum at zero frequency vanishes, we show thatthe critical behavior can be anomalous, i.e. the mode amplitude X scales withdeparture from onset \mu as $<X> ~ \mu^\beta$ with an exponent $\beta$different from its deterministic value. This behavior is observed in a directnumerical simulation of the dynamo instability and our results provide apossible explanation to recent experimental observations.

Anomalous exponents at the onset of an instability