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This article is cited in 109 scientific papers (total in 112 papers)
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.
Received: 03.09.1973
Citation:
R. V. Plykin, “Sources and sinks of $A$-diffeomorphisms of surfaces”, Math. USSR-Sb., 23:2 (1974), 233–253
Linking options:
https://www.mathnet.ru/eng/sm3680https://doi.org/10.1070/SM1974v023n02ABEH001719 https://www.mathnet.ru/eng/sm/v136/i2/p243
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