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We study the asymptotic behaviour of two multiplicative- ($q$-) discretePainlev\'e equations as their respective independent variable goes to infinity.It is shown that the generic asymptotic behaviours are given by ellipticfunctions. We extend the method of averaging to these equations to show thatthe energies are slowly varying. The Picard-Fuchs equation is derived for aspecial case of $q$-P$_{\rm III}$

Elliptic asymptotics in $q$-discrete Painlev\'{e} equations