The topology of basis sets for Smale diffeomorphisms
Sbornik. Mathematics, Tome 13 (1971) no. 2, pp. 297-307
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Diffeomorphisms of a closed surface are considered which satisfy Smale's axiom $A$ and an acyclicity condition. It is shown that if one of its basis sets is one-dimensional, then there is also a zero-dimensional source or sink. As a preliminary, some auxiliary propositions of general character are established concerning sources and sinks of diffeomorphisms satisfying the axiom and the condition above.
Bibliography: 10 titles.
@article{SM_1971_13_2_a6,
author = {R. V. Plykin},
title = {The topology of basis sets for {Smale} diffeomorphisms},
journal = {Sbornik. Mathematics},
pages = {297--307},
publisher = {mathdoc},
volume = {13},
number = {2},
year = {1971},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1971_13_2_a6/}
}
R. V. Plykin. The topology of basis sets for Smale diffeomorphisms. Sbornik. Mathematics, Tome 13 (1971) no. 2, pp. 297-307. http://geodesic.mathdoc.fr/item/SM_1971_13_2_a6/