The topological classification of locally direct product of DA-diffeomorphism of a 2-torus and rough diffeomorphism of the circle
V. Z. Grines1, Yu. A. Levchenko2, O. V. Pochinka3
| Annotation | In this paper we consider a class of diffeomorphisms of 3-manifold, such that each diffeomorphism fron this class is a locally direct product of a DA-diffeomorphism of 2-torus and rough diffeomorphism of the circle. We find algebraic criteria for topological conjugacy of the systems. It is proved that the class of topological conjugacy of such diffeomorphism is completely determined by combinatorial invariants, namely hyperbolic automorphism of the torus, a subset of its periodic orbits, the number of periodic orbits and the serial number of the diffeomorphism of the circle |
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| Keywords | topological conjugacy, DA-diffeomorphism, hyperbolic automorphism |
1Professor of Department of Numerical and Functional Analysis in Nizhny Novgorod State University; vgrines@yandex.ru
2Researcher, Nizhny Novgorod State University; ulev4enko@gmail.com
3Professor of Department of fundamental mathematics of Higher School of Economics; olga-pochinka@yandex.ru
Citation: V. Z. Grines, Yu. A. Levchenko, O. V. Pochinka, "[The topological classification of locally direct product of DA-diffeomorphism of a 2-torus and rough diffeomorphism of the circle]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,17:1 (2015) 30–36 (In Russian)
