Classification of one-dimensional attractors of diffeomorphisms of surfaces by means of pseudo-anosov homeomorphisms
- Authors: Grines V.Z.1, Kurenkov E.D.1
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Affiliations:
- Higher School of Economics
- Issue: Vol 485, No 2 (2019)
- Pages: 135-138
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/12815
- DOI: https://doi.org/10.31857/S0869-56524852135-138
- ID: 12815
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Abstract
In the present paper axiom diffeomorphisms of closed 2-manifolds of genus whose nonwandering set contains perfect spaciously situated one-dimensional attractor are considered. It is shown that such diffeomorphisms are topologically semiconjugate to pseudo-Anosov homeomorphism with the same induced automorphism of fundamental group. The main result of the paper is the following. Two diffeomorphisms from the given class are topologically conjugate on attractors if and only if corresponding pseudo-Anosov homeomorphisms are topologically conjugate by means of homeomorphism that maps a certain subset of one pseudo-Anosov map onto the certain subset of the other pseudo-Anosov map.
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About the authors
V. Z. Grines
Higher School of Economics
Author for correspondence.
Email: vgrines@yandex.ru
Russian Federation, Moscow
E. D. Kurenkov
Higher School of Economics
Email: eugene2402@mail.ru
Russian Federation, Moscow
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