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 Mat. Sb. (N.S.), 1974, Volume 94(136), Number 2(6), Pages 243–264 (Mi msb3680)

Sources and sinks of $A$-diffeomorphisms of surfaces

R. V. Plykin

Abstract: In the present paper the mechanism of the appearance of zero-dimensional sinks and sources in the presence of one-dimensional basic sets of diffeomorphisms of two-dimensional surfaces, satisfying Axiom A, is studied. New examples are constructed of one-dimensional basic sets of structurally stable diffeomorphisms of the two-dimensional sphere. The existence is proved of zero-dimensional sinks and sources of diffeomorphisms of orientable surfaces of genus less than two, which are not $Y$-diffeomorphisms. An estimate is given of the number of amply situated basic sets of $A$-diffeomorphisms of orientable surfaces by means of topological invariants of the surfaces.
Figures: 2.
Bibliography: 17 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 23:2, 233–253

Bibliographic databases:

UDC: 513.83
MSC: Primary 58F15, 15F20; Secondary 54H20, 34C35, 28A65

Citation: R. V. Plykin, “Sources and sinks of $A$-diffeomorphisms of surfaces”, Mat. Sb. (N.S.), 94(136):2(6) (1974), 243–264; Math. USSR-Sb., 23:2 (1974), 233–253

Citation in format AMSBIB
\Bibitem{Ply74} \by R.~V.~Plykin \paper Sources and sinks of $A$-diffeomorphisms of surfaces \jour Mat. Sb. (N.S.) \yr 1974 \vol 94(136) \issue 2(6) \pages 243--264 \mathnet{http://mi.mathnet.ru/msb3680} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=356137} \zmath{https://zbmath.org/?q=an:0324.58013} \transl \jour Math. USSR-Sb. \yr 1974 \vol 23 \issue 2 \pages 233--253 \crossref{https://doi.org/10.1070/SM1974v023n02ABEH001719} 

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