  Analytically tractable dynamical systems exhibiting a whole range of normal
and anomalous deterministic diffusion are rare. Here we introduce a simple
non-chaotic model in terms of an interval exchange transformation suitably
lifted onto the whole real line which preserves distances except at a countable
set of points. This property, which leads to vanishing Lyapunov exponents, is
designed to mimic diffusion in non-chaotic polygonal billiards that give rise
to normal and anomalous diffusion in a fully deterministic setting. As these
billiards are typically too complicated to be analyzed from first principles,
simplified models are needed to identify the minimal ingredients generating the
different transport regimes. For our model, which we call the slicer map, we
calculate all its moments in position analytically under variation of a single
control parameter. We show that the slicer map exhibits a transition from
subdiffusion over normal diffusion to superdiffusion under parameter variation.
Our results may help to understand the delicate parameter dependence of the
type of diffusion generated by polygonal billiards. We argue that in different
parameter regions the transport properties of our simple model match to
different classes of known stochastic processes. This may shed light on
difficulties to match diffusion in polygonal billiards to a single anomalous
stochastic process.
