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JOURNALS // Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva // Archive

Trudy SVMO, 2008, Volume 10, Number 1, Pages 174–180 (Mi svmo90)

In Middle Volga Mathematical Society

On classification of one-dimensional attractors for diffeomorphisms of 3-manifolds

Yu. A. Levchenko

Nizhnii Novgorod State Agricultural Academy

Abstract: We consider $A$-diffeomorphism $f$ of three-manifold $M^3$ with a surface one-dimensional attractor or repeller $\Lambda$ and $ M^2_ \Lambda$ is a locally flat supporting surface for $\Lambda$, for which the set $M^2_{\Lambda}\setminus \lambda$ consist of the finite number of districts. Each district is homeomorfic to standard disk and contain only one periodic point of $A$-diffeomorphism $f$. This paper is devoted to topological classification of restriction $f$ to $M^2_{\Lambda}$.

Keywords: A-diffeomorphism, basic set, attractor, topological classification.

UDC: 513.83



© Steklov Math. Inst. of RAS, 2026