Ellis Group and the Topological Center of the Flow Generated by the Map $${n \mapsto {\lambda^{n}}^{k}}$$

Abstract

For each natural number k and each irrational member λ of the unit circle, it is proved that the shift-orbit closure Xf of the function \({f(n) = {\lambda^{n}}^{k}}\) is homeomorphic to a k-torus. Using this homeomorphism, we investigate the Ellis group and its topological center of the dynamical system (Xf, U), where U is the shift operator on \({l^{\infty}(\mathbb{Z})}\). Finally, it is shown that the topological center of the spectrum of the Weyl algebra is the image of \({\mathbb{Z}}\) in the spectrum.