$$C^{1}$ -Smooth $$\Omega$$ -Stable Skew Products and Completely Geometrically Integrable Self-Maps of 3D-Tori, I：$$\Omega$$ - 稳定性

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Regular and Chaotic Dynamics Pub Date : 2024-05-06 DOI:10.1134/S1560354724520010

Lyudmila S. Efremova

{"title":"$$C^{1}$ -Smooth $$\\Omega$$ -Stable Skew Products and Completely Geometrically Integrable Self-Maps of 3D-Tori, I：$$\\Omega$$ - 稳定性","authors":"Lyudmila S. Efremova","doi":"10.1134/S1560354724520010","DOIUrl":null,"url":null,"abstract":"<div>We prove here the criterion of \$C^{1}\$- \$\\Omega\$-stability of self-maps of a 3D-torus, which\nare skew products of circle maps. The \$C^{1}\$- \$\\Omega\$-stability property is studied with respect to homeomorphisms of skew products type. We give here an example of the \$\\Omega\$-stable map on a 3D-torus and investigate approximating properties of maps under consideration.</div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 3","pages":"491 - 514"},"PeriodicalIF":0.8000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"\\\$C^{1}\\\$-Smooth \\\$\\\\Omega\\\$-Stable Skew Products and Completely Geometrically Integrable Self-Maps of 3D-Tori, I: \\\$\\\\Omega\\\$-Stability\",\"authors\":\"Lyudmila S. Efremova\",\"doi\":\"10.1134/S1560354724520010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>We prove here the criterion of \\\$C^{1}\\\$- \\\$\\\\Omega\\\$-stability of self-maps of a 3D-torus, which\\nare skew products of circle maps. The \\\$C^{1}\\\$- \\\$\\\\Omega\\\$-stability property is studied with respect to homeomorphisms of skew products type. We give here an example of the \\\$\\\\Omega\\\$-stable map on a 3D-torus and investigate approximating properties of maps under consideration.</div>\",\"PeriodicalId\":752,\"journal\":{\"name\":\"Regular and Chaotic Dynamics\",\"volume\":\"29 3\",\"pages\":\"491 - 514\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Regular and Chaotic Dynamics\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1560354724520010\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354724520010","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

我们在这里证明了三维环的自映射的（(C^{1}\)-$\Omega$-稳定性标准，这些自映射是圆映射的偏积。我们研究了斜积类型的同构的(C^{1}\)-$\Omega$-稳定性。我们在这里给出了一个三维副面上的（\ω\）-稳定映射的例子，并研究了所考虑的映射的近似性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

$C^{1}$-Smooth $\Omega$-Stable Skew Products and Completely Geometrically Integrable Self-Maps of 3D-Tori, I: $\Omega$-Stability

We prove here the criterion of $C^{1}$- $\Omega$-stability of self-maps of a 3D-torus, which are skew products of circle maps. The $C^{1}$- $\Omega$-stability property is studied with respect to homeomorphisms of skew products type. We give here an example of the $\Omega$-stable map on a 3D-torus and investigate approximating properties of maps under consideration.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.

期刊最新文献

Rotations and Integrability Higher Symmetries of Lattices in 3D Lagrangian Manifolds in the Theory of Wave Beams and Solutions of the Helmholtz Equation Switching Activity in an Ensemble of Excitable Neurons Synchronization by an External Periodic Force in Ensembles of Globally Coupled Phase Oscillators