Large amplitude oscillatory shear flows of polymer melts between parallel plates may exhibit a complicated non-periodic response characteristic of quasi-periodicity or chaos. This complex time dependence is related to the wall slip exhibited by polymer melts. We use simple models for the fluid elasticity and wall slip to theoretically and computationally study the non-linear dynamics of melts in oscillatory shear. The results indicate that both fluid elasticity and a dynamic (e.g. memory-slip) model for the wall slip are necessary for non-periodic dynamics to occur. Furthermore, when elasticity and a dynamic slip model are coupled, the qualitative dynamics observed in the experiments can be reproduced. Asymmetric periodic responses exhibiting even harmonics are found, as well as quasiperiodic and chaotic motions. Particularly interesting is the prediction of multiple stable periodic motions for a given set of parameters, depending on initial conditions. The existence of complex dynamics is robust with respect to changes in both the constitutive model chosen and the details of the wall slip model.