Ellis group and the topological center of the flow generated by the map \(n\mapsto\lambda^{n^k}\). (Q720026)

The authors study the Ellis group and its topological center of the dynamical system \((X_f,U)\), where \(U\) is the shift operator on \(l^{\infty}(\mathbb{Z})\), \(f(n)=\lambda^{n^k}\) and \(\lambda\) is an irrational number of the unit circle. It is proved that for each natural number \(k\), the shift-orbit closure \(X_f\) of the function \(f\) is homeomorphic to the \(k\)-torus. Further it is shown that the topological center of the spectrum of the Weyl algebra is the image of \(\mathbb{Z}\) in the spectrum.