In Middle Volga Mathematical Society

On classification for diffeomorphisms of 3-dimensional sphere with one-dimensional basis sets

Yu. A. Levchenko

Nizhnii Novgorod State Agricultural Academy

Abstract: We consider $A$-diffeomorphism $f$ of 3-sphere $S^3$ 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 diffeomorphisms satisfying this conditions.

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

UDC: 513.83

Received: 10.09.2008