On topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers
2014, Vol. 10, No. 1, pp. 17-33
Author(s): Grines V. Z., Levchenko Y. A., Pochinka O. V.
We consider a class of diffeomorphisms on 3-manifolds which satisfy S. Smale’s axiom A such that their nonwandering set consists of two-dimensional surface basic sets. Interrelation between dynamics of such diffeomorphism and topology of the ambient manifold is studied. Also we establish that each considered diffeomorphism is Ω-conjugated with a model diffeomorphism of mapping torus. Under certain assumptions on asymptotic properties of two-dimensional invariant manifolds of points from the basic sets, we obtain necessary and sufficient conditions of topological conjugacy of structurally stable diffeomorphisms from the considered class.
Download File PDF, 440.33 Kb |

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License