Geodesic
Expansive Endomorphisms on the Infinite-Dimensional Torus
Funkcionalʹnyj analiz i ego priloženiâ, Tome 54 (2020) no. 4, pp. 17-36

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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 $\mathbb{T}^{\infty}$.
Mots-clés : endomorphism, torus
Keywords: hyperbolicity, topological conjugacy, structural stability, mixing. 
@article{FAA_2020_54_4_a1,
     author = {S. D. Glyzin and A. Yu. Kolesov and N. Kh. Rozov},
     title = {Expansive {Endomorphisms} on the {Infinite-Dimensional} {Torus}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {17--36},
     publisher = {mathdoc},
     volume = {54},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2020_54_4_a1/}
}
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S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Expansive Endomorphisms on the Infinite-Dimensional Torus. Funkcionalʹnyj analiz i ego priloženiâ, Tome 54 (2020) no. 4, pp. 17-36. http://geodesic.mathdoc.fr/item/FAA_2020_54_4_a1/