Ekaterina Chilina


Grines V. Z., Pochinka O. V., Chilina E. E.
The present paper is devoted to a study of orientation-preserving homeomorphisms on three-dimensional manifolds with a non-wandering set consisting of a finite number of surface attractors and repellers. The main results of the paper relate to a class of homeomorphisms for which the restriction of the map to a connected component of the non-wandering set is topologically conjugate to an orientation-preserving pseudo-Anosov homeomorphism. The ambient $\Omega$-conjugacy of a homeomorphism from the class with a locally direct product of a pseudo-Anosov homeomorphism and a rough transformation of the circle is proved. In addition, we prove that the centralizer of a pseudo-Anosov homeomorphisms consists of only pseudo- Anosov and periodic maps.
Keywords: pseudo-Anosov homeomorphism, two-dimensional attractor
Citation: Grines V. Z., Pochinka O. V., Chilina E. E.,  On Homeomorphisms of Three-Dimensional Manifolds with Pseudo-Anosov Attractors and Repellers, Regular and Chaotic Dynamics, 2024, vol. 29, no. 1, pp. 156-173

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