Eugene Osenkov
Bol’shaya Pecherskaya ul. 25/12, Nizhny Novgorod, 603155 Russia
National Research University “Higher School of Economics”
Publications:
|
Osenkov E. M., Pochinka O. V.
Morse – Smale 3-Diffeomorphisms with Saddles of the Same Unstable Manifold Dimension
2024, Vol. 20, no. 1, pp. 167-178
Abstract
In this paper, we consider a class of Morse – Smale diffeomorphisms defined on a closed
3-manifold (not 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. As Reeb showed back in 1946, such systems can
only be realized 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.
|