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 \(N\ge 2\) .