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

We study the asymptotic behaviour of two multiplicative- ($q$-) discrete Painlevu0027e equations as their respective independent variable goes to infinity. It is shown that the generic asymptotic behaviours are given by elliptic functions. We extend the method of averaging to these equations to show that the energies are slowly varying. The Picard-Fuchs equation is derived for a special case of $q$-P$_{rm III}$