Classification of Partial Hyperbolic Diffeomorphisms on 3-manifolds

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Tahuri Turki, Ata | 2022

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 55350 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Safdari, Mohammad; Nassiri, Meysam
Abstract:
In this dissertation, we will study partially hyperbolic diffeomorphisms. First, we are going to introduce partially hyperbolic diffeomorphisms and construct some examples. One of the important questions in the study of partially hyperbolic diffeomorphisms is their classification problem, which provides a deeper understanding of manifolds and also of partially hyperbolic diffeomorphisms themselves. We will go through this problem by examining Hammerlindl, Potrie’s [1]’s work. They have proved that a partially hyperbolic diffeomorphism on a 3-manifold with a virtually solvable fundamental group, that has no periodic torus tangent to contraction-center or expansion-center, is dynamically coherent. Also, they have proved that there exists a finite iterate of this diffeomorphism which is leaf conjugate to the time-one map of a suspension Anosov flow.
Keywords:
Foliation ; Fundamental Group Representation ; Flow Time-One Map ; Suspension Manifold ; Anosov Flow ; Branching Foliation ; Partially Hyperbolic Diffeomorphisms

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