A kind of symbolic dynamical systems describing non-chaotic maps (Q1902259)

The author considers the odometer transformation of \(\{0, 1\}^{\mathbb{Z}^+}\) and establishes some basic properties. He then introduces a piecewise linear map \(T\) of the interval with infinitely many branches and shows that there is a subset of the interval on which the dynamics is conjugate to the odometer. He points out that the example can be embedded in a homeomorphism of \(\mathbb{R}^2\).