  An important aspect of the physics of amorphous solids is the onset of
irreversible behavior usually associated with yield. Here we study amorphous
solids under periodic shear using quasi-static molecular dynamics simulations
and observe a transition from reversible to irreversible deformation at a
critical strain amplitude. We find that for small strain amplitudes the system
exhibits a noisy but repetitive limit-cycle, similar to return point memory
\cite{sethna1993hysteresis}. However, for large strain amplitudes the behavior
becomes chaotic (shows sensitivity to initial conditions) and thus
irreversible. We show that the chaotic behavior is a result of the shear band
instabilities that arise for large strains and the convective displacement
fields they create.
