# Cylinder transformation

Let $\mathbb{T}$ be a time scale. We define the cylinder transformation $\xi_h \colon \mathbb{C}_h \rightarrow \mathbb{Z}_h$, where $\mathbb{C}_h$ denotes the Hilger complex plane and $\mathbb{Z}_h$ denotes the cylinder strip, and is defined by the formula $$\xi_h(z)=\dfrac{1}{h} \mathrm{Log}(1+zh),$$ where $\mathrm{Log}$ denotes the principal logarithm.