We study the Euler operator on $R^{n}$ from the point of view of Noncommutative Geometry. The operator defines, roughly, an equivariant spectral triple over the Samuel compactification of $R^{n}$, and as the Samuel compactification is universal with respect to minimal flows, one gets from this construction a variety of examples of spectral cycles in connection with minimal linear dynamical systems. The associated index data and zeta functions of these triples seem quite interesting, and the zeta functions especially pose several problems, which I will describe.