Multi-dimensional hyperbolic chaos

We propose a mathematical model for a new phenomenon: multi-dimensional hyperbolic chaos. This model is a ring chain of $N\geqslant 2$ unidirectionally coupled maps of the two-dimensional torus $\mathbb{T}^2$, each of which is of Arnold's cat map type. We provide sufficient conditions (independent of $N$) under which the chain gives rise to an Anosov diffeomorphism of $\mathbb{T}^{2N}$ for any $N\geqslant 2$.