The Pell Tower and Ostronometry

Conway and Ryba considered a table of bi-infinite Fibonacci sequences and discovered new interesting patterns. We extend their considerations to tables that are defined by the recurrence $X_{n+1}=dX_n+X_{n-1}$ for natural numbers $d$. In our search for new patterns we run into a Red Wall and exotic numeration systems

Self-duality and codings for expansive automorphisms

AbstractLind and Schmidt have shown that for certain ergodic Zk-actions on a compact abelian group Γ, the homoclinic group H is isomorphic to the Pontryagin dual of Γ. Einsiedler and Schmidt extended these results and showed that Γ is a quotient of a locally compact ring R modulo H. In this paper, we present a dynamical interpretation of R if k=1: it is a product of the stable group and the unstable group of Γ, under a suitable topology. As applications, we give a topological interpretation of the Pisot–Vijayaraghavan theorem and we link the results to tessellation theory