We study a quite natural class of diffeomorphisms on , where is the infinite-dimensional torus (the direct product of countably many circles endowed with the topology of uniform coordinatewise convergence). The diffeomorphisms under consideration can be represented as the sums of a linear hyperbolic map and a periodic additional term. We find some constructive sufficient conditions, which imply that any in our class is hyperbolic, that is, an Anosov diffeomorphism on . Moreover, under these conditions we prove the following properties standard in the hyperbolic theory: the existence of stable and unstable invariant foliations, the topological conjugacy to a linear hyperbolic automorphism of the torus and the structural stability of .

我们研究了很自然类微分同胚上，这里是无限维圆环（可数个圈赋予了统一的coordinatewise收敛的拓扑结构的直接产物）。所考虑的微分同胚可以表示为线性双曲线映射和周期性附加项的总和。我们找到了一些建设性的充分条件，这意味着我们类中的任何一个都是双曲的，即 上的 Anosov 微分同胚。此外，在这些条件下，我们证明了双曲理论中的以下性质标准：稳定和不稳定的不变叶理的存在，对环面的线性双曲自同构的拓扑共轭和 的结构稳定性。