Multi-Dimensional Hyperbolic Chaos

We propose a mathematical model for a new phenomenon: multi-dimensional hyperbolic chaos. This model is a ring chain of $$N\ge 2$$ 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 $$N\ge 2$$ .