Strange attractors. Topologic, geometric and algebraic aspects
Strange attractors. Topologic, geometric and algebraic aspects
复制标题
奇怪的吸引子。
DOI：
10.1134/s156035471002019x
复制
发表时间：
2010
影响因子：
1.4
通讯作者：
N. Klinshpont
中科院分区：
文献类型：
--
作者：
R. V. Plykin;N. Klinshpont
本文综述了两位作者对双曲型和Lorenz型奇异吸引子的研究工作。1971年R.普利金收到了一封信，从两个年轻的科学家沃里克大学大卫齐灵沃斯和安东尼曼宁指出他的错误，在文章中题为“拓扑结构的基本集的斯梅尔同构”。这篇文章的主要错误是关于双球面同态的一维双曲吸引子不存在的说法。本文第一部分纠正了以前的错误，并介绍了双曲奇异吸引子的几何和拓扑结构。Klinshpont关于Lorenz型吸引子的拓扑分类问题及其推广.对可微动力系统的随机性质的研究往往导致对其他极限形式的研究，而对这些极限形式的分离是一个困难的问题，它不仅需要分析和几何方法，而且需要大量的计算资源.在几何方法中，这一研究遵循，流形与其上的动力系统一起研究，其中吸引子的结构具有多样性，主要困难是分类问题。
This article is a review on research work of two authors on hyperbolic and Lorenz like strange attractors. In 1971 R. Plykin received a letter from two young scientists of Warwick University David Chillingworth and Anthony Manning with pointing out his errors in the article entitled “The topology of basic sets for Smale diffeomorphisms”. The main error in that manuscript was the statement about nonexistence of one dimensional hyperbolic attractor of the diffeomorphism of two-sphere. The first part of this report corrects previous errors and carries information about geometry and topology of hyperbolic strange attractors.The second part of the report contains some results obtained by N. Klinshpont on the problem of topological classification of Lorenz type attractors and their generalizations.An investigation of stochastic properties of differentiable dynamical systems often results in study other limiting formations, the isolation of which is a difficult problem which requires the mobilization of not only analytical and geometrical methods but also substantial computational resources.In the geometrical approach, which this investigation follows, manifolds are studied together with dynamical systems on them in which the diversity of structures of attractors occurs and the main difficulties are the classification problems.