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- W4387635835 abstract "In this paper, we consider a class of Morse-Smale diffeomorphisms defined on a closed 3-manifold (non-necessarily orientable) under the assumption that all their saddle points have the same dimension of the unstable manifolds. The simplest example of such diffeomorphisms is the well-known ``source-sink'' or ``north pole - south pole'' diffeomorphism, whose non-wandering set consists of exactly one source and one sink. Such systems, as Reeb showed back in 1946, can be realized only on the sphere. We generalize his result, namely, we show that diffeomorphisms from the considered class also can be defined only on the 3-sphere." @default.
- W4387635835 created "2023-10-14" @default.
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- W4387635835 creator A5093063152 @default.
- W4387635835 date "2023-10-12" @default.
- W4387635835 modified "2023-10-15" @default.
- W4387635835 title "Morse-Smale 3-diffeomorphisms with saddles of the same unstable manifold dimension" @default.
- W4387635835 doi "https://doi.org/10.48550/arxiv.2310.08476" @default.
- W4387635835 hasPublicationYear "2023" @default.
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