  We consider equivariant continuous families of discrete one-dimensional
operators over arbitrary dynamical systems. We introduce the concept of a
pseudo-ergodic element of a dynamical system. We then show that all operators
associated to pseudo-ergodic elements have the same spectrum and that this
spectrum agrees with their essential spectrum. As a consequence we obtain that
the spectrum is constant and agrees with the essential spectrum for all
elements in the dynamical system if minimality holds.
