  The heterochaos baker maps are piecewise affine maps of the unit square or
cube introduced by Saiki et al. (2018), to provide a hands-on, elementary
understanding of complicated phenomena in systems of large degrees of freedom.
We review recent progress on a dynamical systems theory of the heterochaos
baker maps, and present new results on properties of measures of maximal
entropy and the underlying Lebesgue measure. We address several conjectures and
questions that may illuminate new aspects of heterochaos and inspire future
research.
