In this paper we give a complete classification of the infinite Schreier graphs of an automaton group generated by an extended version of the binary adding machine.

we describe under various conditions abelian subgroups of the automorphism‎ ‎group $mathrm{aut}(t_{n})$ of the regular $n$-ary tree $t_{n}$‎, ‎which are‎ ‎normalized by the $n$-ary adding machine $tau =(e‎, ‎dots‎, ‎e,tau )sigma _{tau‎ ‎}$ where $sigma _{tau }$ is the $n$-cycle $left( 0,1‎, ‎dots‎, ‎n-1right) $‎. ‎as‎ ‎an application‎, ‎for $n=p$ a prime number‎, ‎and for $n=4$‎, ‎we prove that...

We prove two theorems which extend known results concerning periodic orbits and topological entropy in one-dimensional dynamics. One of these results concerns the adding machine map (also called the odometer map) fα defined on the α-adic adding machine ∆α. We let H(fα) denote the greatest lower bound of the topological entropies of F , taken over all continuous maps F of the interval which cont...

We show that given a type α of an adding machine, for a dense set of parameters s in the interval [ √ 2, 2], if f is the tent map with slope s, then the restriction of f to the closure of the orbit of the turning point is topologically conjugate to the adding machine map of type α.

It is well-known that stable Cantor sets are topologically conjugate to adding machines. In this work we show are also conjugate to an algebraic object, the ring of P−adic integers with respect to group tramnslation. This ring is closely related to the field of p-adic numbers; connections and distintions are explored. The inverse limit construction provides a purely dynamical proof of an algebr...

Semantic and semi-structured wiki implementations, which extend traditional, purely string-based wikis by adding machine-processable metadata, suffer from a lack of support for media management. Currently, it is difficult to maintain semantically rich metadata for both wiki pages and associated media assets; media management functionalities are cumbersome or missing. With Ylvi, a semantic wiki ...

We describe under various conditions abelian subgroups of the automorphism group Aut(Tn) of the regular n-ary tree Tn, which are normalized by the n-ary adding machine τ = (e, . . . , e, τ)στ where στ is the n-cycle (0, 1, . . . , n− 1). As an application, for n = p a prime number, and for n = 4, we prove that every soluble subgroup of Aut(Tn), containing τ is an extension of a torsion-free met...

Here we build on the result given in [P1] and extend those in [HL2] to functions which are k times differentiable a.e., k > 1. For each k we give, a class of irrational number Sk such that the skew product extension defined by these functions is ergodic for irrational rotations by these numbers. In the second part of this paper we examine the cohomology of functions over the adding machine tran...

The notion of computing seems nowadays to be so synonymous with computers, that we often seem to forget that electronic computers are relatively new players on the world stage, [31]. Indeed, a brief look at the history of humanity shows that since the earliest days people needed to count and compute, either for measuring the months and the seasons or for commerce and constructions. The means us...