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Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2011, Volume 13, Number 2, Pages 17–24
(Mi svmo233)
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Complete topological invariant for Morse-Smale
diffeomorphisms on 3-manifolds
O. V. Pochinka N. I. Lobachevski State University of Nizhni Novgorod
Abstract:
The present paper is devoted
to topological classification of a set $G(M^3)$ of preserving
orientation Morse-Smale diffeomorphisms $f$ given on smooth closed
orientable 3-manifolds $M^3$. A complete topological invariant for
a diffeomorphism $f\in G(M^3)$ is equivalence class of its scheme
$S_f$, which contains an information on periodic dates and on
topology of embedding in ambient manifold of two-dimensional
invariant manifolds of the saddle periodic points of $f$.
Moreover, it is introduced a set $\mathcal S$ of abstract schemes,
having a representative from each equivalence class of schemes of
the diffeomorphisms from $G(M^3)$ and it is constructed a
diffeomorphism $f_S\in G(M^3)$ whose scheme is equivalent to
$S$.
Keywords:
morse-Smale diffeomorphisms, topological classification,
orbit space.
Received: 24.06.2011
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Abstract page: | 49 | References: | 4 |
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