Two odometers in honeybees?

Linear Recursive Odometers and Beta-expansions

The aim of this paper is to study the connection between different properties related to β-expansions. In particular, the relation between two conditions, both ensuring pure discrete spectrum of the odometer, is analysed. The first one is the so-called Hypothesis B for the G-odometers and the second one is denoted by (QM) and it has been introduced in the framework of tilings associated to Piso...

The spatial structure of odometers in certain cellular automata

Recent work has shown that many cellular automata (CA) have configurations whose orbit closures are isomorphic to odometers. We investigate the geometry of the spacetime diagrams of these ‘odometer configurations’. For boolean linear CA, we exactly determine the positions of the consecutive ‘gears’ of the odometer mechanism in the configuration. Then we characterize and explain the self-similar...

On-Line Odometers for Two-Sided Symbolic Dynamical Systems

Embedding Odometers in Cellular Automata

We consider the problem of embedding odometers in one-dimensional cellular automata. We show that (1) every odometer can be be embedded in a gliders with reflecting walls cellular automaton, which one depending on the odometer, and (2) an odometer can be embedded in a cellular automaton with local rule xi 7→ xi + xi+1 mod n (i ∈ Z), where n depends on the odometer, if and only if it is “finitary.”

Dimension Groups and Invariant Measures for Polynomial Odometers

Adic maps on simple ordered Bratteli diagrams, called Bratteli-Vershik systems, have been proven to be extremely useful as models for minimal Cantor systems. In particular, the dimension group given by the diagram is order isomorphic to the ordered cohomology group for the system, and this along with a distinguished order unit is shown to be the complete invariant for strong orbit equivalence i...