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In order to describe the asymptotic behaviour of a vanishing period in a oneparameter family we introduce and use a very simple algebraic structure :regular geometric (a,b)-modules generated (as left $\A-$modules) by oneelement. The idea is to use not the full Brieskorn module associated to theGauss-Manin connection but a minimal (regular) differential equation satisfiedby the period integral we are interested in. We show that the Bernsteinpolynomial associated is quite simple to compute for such (a,b)-modules andgive a precise description of the exponents which appears in the asymptoticexpansion which avoids integral shifts. We show a couple of explicitcomputations in some classical (but not so easy) examples.

P\'eriodes \'evanescentes et $(a,b)$-modules monog\`enes