2-Torus 的梯度样差变形的稳定同位连接性

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-10-31 DOI:10.1016/j.geomphys.2024.105352

A.A. Nozdrinov, E.V. Nozdrinova, O.V. Pochinka

引用次数: 0

摘要

动力系统理论中最重要的问题之一（在帕里斯-普列表中提到）是在差分空间中构造结构稳定的差分变形之间的稳定弧。本文研究了诱发由矩阵 (-100-1) 决定的基本群同构的 2-Torus 的梯度样差分。我们证明了所有这样的差分同构都是稳定的等位连接。

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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Stable isotopy connectivity of gradient-like diffeomorphisms of 2-torus

One of the most important problems in the theory of dynamical systems (mentioned in the Palis-Pugh list) is the construction of a stable arc between structural stable diffeomorphisms in the space of diffeomorphisms. The paper considers the gradient-like diffeomorphisms of 2-torus that induce an isomorphism of fundamental groups determined by a matrix

(\begin{matrix} - 1 & 0 \\ 0 & - 1 \end{matrix})

. We prove that all such diffeomorphisms are stable isotopy connected.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity