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Measuring geodesics’ aperiodicity


Mätzener, Anna. Measuring geodesics’ aperiodicity. 2011, University of Zurich, Faculty of Science.

Abstract

Aperiodicity can arise both in the setting of sequences over a finite alphabet, and that of geodesics on a compact Riemannian surface. In both cases, aperiodicity itself provides no means to measure and compare different aperiodic objects one to another. For sequences the notion of -aperiodicity, by the function , provides a means for this. The aim of this thesis was to find an analogon in the setting of geodesics. This was done by defining f-aperiodicity of geodesics. The existence of f-aperiodic geodesics was proven for a very specific setting, namely that of a quotient of the hyperbolic surface of H. This quotient was chosen in a specific way, such that a -aperiodic sequence could be chosen as the origin in the construction of the geodesic. Furthermore, this led to an easy way to define a flow-invariant subset of the unit tangent bundle of the compact Riemannian surface.

Abstract

Aperiodicity can arise both in the setting of sequences over a finite alphabet, and that of geodesics on a compact Riemannian surface. In both cases, aperiodicity itself provides no means to measure and compare different aperiodic objects one to another. For sequences the notion of -aperiodicity, by the function , provides a means for this. The aim of this thesis was to find an analogon in the setting of geodesics. This was done by defining f-aperiodicity of geodesics. The existence of f-aperiodic geodesics was proven for a very specific setting, namely that of a quotient of the hyperbolic surface of H. This quotient was chosen in a specific way, such that a -aperiodic sequence could be chosen as the origin in the construction of the geodesic. Furthermore, this led to an easy way to define a flow-invariant subset of the unit tangent bundle of the compact Riemannian surface.

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Additional indexing

Item Type:Dissertation
Referees:Schroeder Viktor, Kappeler Thomas
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2011
Deposited On:14 Aug 2012 08:17
Last Modified:05 Apr 2016 15:55
Number of Pages:53
Related URLs:http://opac.nebis.ch/F/?local_base=EBI01&con_lng=GER&func=find-b&find_code=090&request=002033141

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