Beckus, SiegfriedSiegfriedBeckusLenz, DanielDanielLenzLindner, MarkoMarkoLindnerSeifert, ChristianChristianSeifert2019-07-122019-07-122018-05-01Proceedings of the Edinburgh Mathematical Society 2 (61): 371-386 (2018-05-01)http://hdl.handle.net/11420/2942We 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.en0013-091520182371386Journal Article10.1017/S0013091517000086Other