On topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers

Vyacheslav Z. Grines ; Yulia A. Levchenko ; Olga V. Pochinka

Russian journal of nonlinear dynamics, Tome 10 (2014) no. 1, pp. 17-33.

Résumé

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 $\Omega$-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.

Détail

Keywords: diffeomorphism, basic set, topological conjugacy, attractor, repeller.

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