Multidimensional hyperbolic chaos

A mathematical model of a new phenomenon – multidimensional hyperbolic chaos – is proposed. This model is a ring chain of $N \geq 2$ unidirectionally coupled maps of a two-dimensional torus $\mathbb{T}^{2}$ of "Arnold's cat" type. Some sufficient conditions (independent of $N$) are established, under which for any positive integer $N \geq 2$ the chain under consideration generates an Anosov diffeomorphism on the torus $\mathbb{T}^{2N}$.