Multi-Dimensional Hyperbolic Chaos

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2025-01-20 DOI:10.1134/S0016266324040014

Sergey Glyzin, A. Yu. Kolesov

引用次数: 0

Abstract

We propose a mathematical model for a new phenomenon: multi-dimensional hyperbolic chaos. This model is a ring chain of \(N\ge 2\) unidirectionally coupled maps of the two-dimensional torus \(\mathbb{T}^2\), each of which is of Arnold’s cat map type. We provide sufficient conditions (independent of \(N\)) under which the chain gives rise to an Anosov diffeomorphism of \(\mathbb{T}^{2N}\) for any \(N\ge 2\).

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多维双曲混沌

我们提出了一个新现象的数学模型：多维双曲混沌。这个模型是一个环形链\(N\ge 2\)单向耦合的二维环面\(\mathbb{T}^2\)图，每个都是Arnold的cat图类型。我们提供了充分条件（独立于\(N\)），在此条件下链对任意\(N\ge 2\)产生\(\mathbb{T}^{2N}\)的Anosov微分同构。

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

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.