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Diophantine properties of groups of toral automorphisms

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Title: Diophantine properties of groups of toral automorphisms
Author(s): Finkelshtein, Vladimir
Advisor(s): Furman, Alex
Contributor(s): Groves, Daniel; Whyte, Kevin; Hurder, Steve; Hartman, Yair; Furman, Alex
Department / Program: Mathematics, Statistics and Computer Science
Degree Granting Institution: University of Illinois at Chicago
Degree: PhD, Doctor of Philosophy
Genre: Doctoral
Subject(s): diophantine approximation, spectral gap, hyperbolic groups
Abstract: This dissertation studies a shrinking target problem for the action of an arbitrary subgroup of SL(2,Z) on the 2-torus. This can also be viewed as a non-commutative Diophantine approximation problem. The methods require construction of spectrally optimal random walks on groups acting properly cocompactly on Gromov hyperbolic spaces. Additionally, similar estimates for this problem in higher dimension can be obtained by using harmonic analysis.
Issue Date: 2017-06-06
Type: Thesis
URI: http://hdl.handle.net/10027/21992
Date Available in INDIGO: 2017-11-01
Date Deposited: August 201
 

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