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arXiv · 2312.12083

On homeomorphisms of three-dimensional manifolds with pseudo-Anosov attractors and repellers

Vyacheslav Grines·Olga Pochinka·Ekaterina Chilina
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Abstract

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 $Ω$-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.

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Vyacheslav Grines, Olga Pochinka, Ekaterina Chilina. 2023-12-19. On homeomorphisms of three-dimensional manifolds with pseudo-Anosov attractors and repellers. https://arxiv.org/abs/2312.12083

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