A hyperbolicity criterion for a class of diffeomorphisms of an infinite-dimensional torus

IF 0.8 4区数学 Q2 MATHEMATICS Sbornik Mathematics Pub Date : 2022-01-01 DOI:10.1070/SM9535

S. Glyzin, A. Kolesov

引用次数: 1

Abstract

On an infinite-dimensional torus , where is an infinite-dimensional real Banach space and is an abstract integer lattice, a special class of diffeomorphisms is considered. It consists of the maps equal to sums of invertible bounded linear operators preserving and -smooth periodic additives. Necessary and sufficient conditions ensuring that such maps are hyperbolic (that is, are Anosov diffeomorphisms) are obtained. Bibliography: 15 titles.

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一类无限维环面微分同态的双曲性判据

在无限维环面上，考虑了一类特殊的微分同态，其中无限维实巴拿赫空间为抽象整数格。它由可逆有界线性算子和-光滑周期加法的映射组成。得到了保证这种映射是双曲的(即是ananosov微分同态)的充分必要条件。参考书目:15篇。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis

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