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JOURNALS // Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva // Archive

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

This article is cited 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.

UDC: 513.83



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