1974•Mathematics of the USSR-SbornikRequires access

SOURCES AND SINKS OFA-DIFFEOMORPHISMS OF SURFACES

Romen Vasilievich 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 items.

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Key concepts: Axiom, Mathematics, Zero (linguistics), Pure mathematics, Surface (topology), Genus, Partition (number theory), Situated