There are No Structural Stable Axiom A 3-Diffeomorphisms with Dynamics "One-dimensional Surfaced Attractor-repeller"

被引：1
|
作者：
Pochinka, O. [1 ]
机构：
[1] HSE Univ, DSA Lab, Moscow, Russia
来源：
RESULTS IN MATHEMATICS | 2023年 / 78卷 / 02期
基金：
俄罗斯科学基金会;
关键词：
Structural stability; attractor; repeller; TOPOLOGICAL CLASSIFICATION; DIFFEOMORPHISMS;
D O I：
10.1007/s00025-022-01824-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the structural stability of three-dimensional diffeomorphisms with source-sink dynamics. Here the role of source and sink is played by one-dimensional hyperbolic repeller and attractor. It is well known that in the case when the repeller and the attractor are solenoids (not embedded in the surface), the diffeomorphism is not structurally stable. The author proves that in the case when the attractor and the repeller are canonically embedded in a surface, the diffeomorphism is also not structurally stable.
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页数：21
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