English

There are no structural stable Axiom A 3-diffeomorphisms with dynamics "one-dimensional surfaced attractor-repeller"

Dynamical Systems 2021-11-08 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2108.12996,
  title  = {There are no structural stable Axiom A 3-diffeomorphisms with dynamics "one-dimensional surfaced attractor-repeller"},
  author = {Olga Pochinka},
  journal= {arXiv preprint arXiv:2108.12996},
  year   = {2021}
}

Comments

21 pages, 18 figures

R2 v1 2026-06-24T05:30:52.631Z