作为动力系统吸引子障碍的不变量及其在非整体力学中的作用

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Regular and Chaotic Dynamics Pub Date : 2024-09-05 DOI:10.1134/S156035472456003X

Luis C. García-Naranjo, Rafael Ortega, Antonio J. Ureña

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引用次数: 0

摘要

然后，我们考虑了经典非全局苏斯洛夫问题的广义化，该问题表明，如果我们希望确定吸引子存在的动力学障碍，那么之前对非全局系统不变度量存在性的研究必然要扩展到具有严格正\(C^{1}\)密度的度量类别之外。

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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Invariant Measures as Obstructions to Attractors in Dynamical Systems and Their Role in Nonholonomic Mechanics

We present some results on the absence of a wide class of invariant measures for dynamical systems possessing attractors. We then consider a generalization of the classical nonholonomic Suslov problem which shows how previous investigations of existence of invariant measures for nonholonomic systems should necessarily be extended beyond the class of measures with strictly positive \(C^{1}\) densities if one wishes to determine dynamical obstructions to the presence of attractors.

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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.