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Soit F:V n →R m une application algebrique reelle et D⊂R m l'ensemble de ses valeurs critiques. On etudie la monodromie reelle des applications F definies sur une variete symplectique (V 2m ,ω) et dont les fibres generiques sont lagrangiennes pour la forme symplectique ω. De tels applications sont des applications impulsion de systemes hamiltoniens integrables

The Arnol′d formula for algebraically completely integrable systems