Expansive Endomorphisms on the Infinite-Dimensional Torus

A natural class of expansive endomorphisms $G\in C^1$ of the infinite-dimensional torus $\mathbb{T}^{\infty}$ (the Cartesian product of countably many circles with the product topology) is considered. The endomorphisms in this class can be represented in the form of the sum of a linear expansion and a periodic addition. The following standard facts of hyperbolic theory are proved: the topological conjugacy of any expansive endomorphism $G$ from the class under consideration to a linear endomorphism of the torus, the structural stability of $G$, and the topological mixing property of $G$ on $\mathbb{T}^{\infty}$.