A Geometric Model for Pseudohyperbolic Shilnikov Attractors

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2025-04-07 DOI:10.1134/S1560354725020029

Dmitry Turaev

引用次数: 0

Abstract

We describe a \(C^{1}\)-open set of systems of differential equations in \(R^{n}\), for any \(n\geqslant 4\), where every system has a chain-transitive chaotic attractor which contains a saddle-focus equilibrium with a two-dimensional unstable manifold. The attractor also includes a wild hyperbolic set and a heterodimensional cycle involving hyperbolic sets with different numbers of positive Lyapunov exponents.

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伪双曲希尔尼科夫吸引力的几何模型

我们在\(R^{n}\)中描述了一个\(C^{1}\) -开的微分方程系统集，对于任意\(n\geqslant 4\)，其中每个系统都有一个链传递混沌吸引子，该吸引子包含一个带二维不稳定流形的鞍-焦点平衡。吸引子还包括一个野生双曲集和一个异维循环，其中双曲集具有不同数目的正Lyapunov指数。

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

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.