数学
匡威
吸引子
传递关系
双曲流形
耗散系统
矢量场
双曲3流形
膨胀的
双曲平衡点
纯数学
数学分析
集合(抽象数据类型)
开放集
相对双曲群
双曲函数
几何学
组合数学
计算机科学
物理
抗压强度
材料科学
量子力学
程序设计语言
复合材料
作者
Vı́tor Araújo,Junilson Cerqueira
出处
期刊:Moscow Mathematical Journal
[National Research University, Higher School of Economics (HSE)]
日期:2023-02-01
卷期号:23 (1): 11-46
被引量:1
标识
DOI:10.17323/1609-4514-2023-23-1-11-46
摘要
We prove that sectional-hyperbolic attracting sets for $C^1$ vector fields are robustly expansive (under an open technical condition of strong dissipative for higher codimensional cases). This extends known results of expansiveness for singular-hyperbolic attractors in $3$-flows even in this low dimensional setting. We deduce some converse results taking advantage of recent progress in the study of star vector fields: a robustly transitive attractor is sectional-hyperbolic if, and only if, it is robustly expansive. In a low dimensional setting, we show that an attracting set of a $3$-flow is singular-hyperbolic if, and only if, it is robustly chaotic (robustly sensitive to initial conditions).
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