Abstract For an arbitrary expanding endomorphism of the class $$C^1 $$ acting from $$\mathbb {T}^{\infty } $$ to $$\mathbb {T}^{\infty } $$ , where $$\mathbb {T}^{\infty } $$ is an infinite-dimensional torus (the quotient space of some Banach space by an integer lattice), we establish the following standard assertions from the hyperbolic theory: the topological conjugacy of this endomorphism with the linear endomorphism of the torus and its structural stability, as well as the presence of the property of topological mixing for this endomorphism if the fundamental set of the torus is bounded.

中文翻译：

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无限维环面上的一类结构稳定内同态

Abstract 对于类 $$C^1 $$ 的任意扩展自同态，从 $$\mathbb {T}^{\infty } $$ 到 $$\mathbb {T}^{\infty } $$ ，其中 $ $\mathbb {T}^{\infty } $$ 是一个无限维环面（一些 Banach 空间与整数格的商空间），我们从双曲理论中建立以下标准断言：这种自同态的拓扑共轭环面的线性自同态及其结构稳定性，以及如果环面的基本集是有界的，这种自同态的拓扑混合性质的存在。