Morse-Smale diffeomorphisms with three fixed points
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}}
Morse-Smale diffeomorphism with three fixed points
scientific article; zbMATH DE number 6123760
scientific article