Morse-Smale diffeomorphisms with three fixed points
type: Item
instance of: scholarly article
title: Morse-Smale diffeomorphisms with three fixed points
zbMATH Open document ID: 1280.37030
DOI: 10.1134/S0001434612090222
author: Vladislav S. Medvedev
author: Evgenii V. Zhuzhoma
published in: Mathematical Notes
publication date: 2013-01-09T00:00:00Z
review text: This paper studies Morse-Smale diffeomorphisms with three fixed points and, in particular, if the topological closure of a separatrix of the saddle point can be wildly embedded. The main theorem of the paper reads as follows: Suppose that \(f: M^n \to M^n\) is a Morse-Smale diffeomorphism of a closed manifold of dimension \(n\geq 4\) with three fixed points (a sink, a source and a saddle). Then: {\parindent= 0.5 cm \begin{itemize} \item[a)] \(M^n\) is orientable. \item [b)] The separatices of the saddle have the same dimension. \item [c)] The closures of the stable and the unstable separatrices are topologically embedded \(n/2\)-spheres. \item [d)] If \(n\geq6\), these spheres are locally flat. \item [e)] If \(n=4\), there exists an \(f: M^4 \to M^4\) for which the spheres are wildly embedded. \end{itemize}}
Mathematics Subject Classification ID: 37D15
Mathematics Subject Classification ID: 57R50
zbMATH DE Number: 6123760
zbMATH Keywords: Morse-Smale diffeomorphism with three fixed points
zbMATH Keywords: embedded spheres
reviewed by: J. A. Langa
MaRDI profile type: Publication
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full work available at URL: s0001434612090222
OpenAlex ID: W1979849671
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description: scientific article; zbMATH DE number 6123760