There are no structural stable Axiom A 3-diffeomorphisms with dynamics "one-dimensional surfaced attractor-repeller"
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Publication:6376301
DOI10.1007/S00025-022-01824-ZarXiv2108.12996MaRDI QIDQ6376301
Publication date: 30 August 2021
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.
Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Generic properties, structural stability of dynamical systems (37C20) Stability theory for smooth dynamical systems (37C75)
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