Metrizable extensions of dynamical systems from function algebras

Peters and Pennings introduced and studied in [9] and [11] a kind of extensions of dynamical systems induced by certain C^*-algebras, which they calltame extensions. In this paper we study the behaviour of metrizable tame extensions when some of the most important dynamical concepts related to the metric (such as sources, sinks, saddles, the shadowing property and distallity) are considered. We will confirm that these extensions can be troublesome in this context. We show, however, that sources and sinks are preserved under certain conditions. Entrata in Redazione il 24 febbraio 1997. Research partially supported by Generalitat Valenciana, (2223/94).