$$C^{1}$ -Smooth $$\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

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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。

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$C^{1}$-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.

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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.