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Zhurnal SVMO, 2010, Volume 12, Number 2, Pages 7–13 (Mi svmo74)  

This article is cited in 2 scientific papers (total in 2 papers)

On structure of 3-manifold which allow A-diffeomorphism with two-dimensional surface nonwandering set

V. Z. Grinesa, Yu. A. Levchenkoa, V. S. Medvedevb

a Nizhnii Novgorod State Agricultural Academy
b Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod

Abstract: We consider a class of diffeomorphism satisfying to S.Smale Axiom $A$ given on $3$-manifold $M^3$ on suggestion that nonwandering set of diffeomorphisms consists of connected two-dimensional surface attractor and repellors. We establish that $M^3$ is a locally-trivial foliation under the circle with leaves homeomorphic to the torus.

Keywords: A-diffeomorphism, attractor, repeller, nonwandering set.

References: PDF file   HTML file
UDC: 513.83

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    This publication is cited in the following articles:
    1. V. Z. Grines, Yu. A. Levchenko, O. V. Pochinka, “O topologicheskoi klassifikatsii diffeomorfizmov na 3-mnogoobraziyakh s poverkhnostnymi dvumernymi attraktorami i repellerami”, Nelineinaya dinam., 10:1 (2014), 17–33  mathnet
    2. V. Z. Grines, Yu. A. Levchenko, O. V. Pochinka, “Topological Classification of Structurally Stable 3-Diffeomorphisms with Two-Dimensional Basis Sets”, Math. Notes, 97:2 (2015), 304–306  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
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