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Explicit Examples of Coding Geodesics on Surfaces of Constant Negative Curvature : 음곡률을 가지는 곡면의 측지선 코딩

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Authors

김수진

Advisor
임선희
Major
자연과학대학 수리과학부
Issue Date
2014-02
Publisher
서울대학교 대학원
Keywords
geodesic codingsymbolic dynamics
Description
학위논문 (석사)-- 서울대학교 대학원 : 수리과학부, 2014. 2. 임선희.
Abstract
It is well-known that there are various ways of representing geodesics on a surface M of constant negative curvature. There are two different methods on the bottom line: one is geometric coding and the other is arithmetic coding. The former is the so-called Morse method which is coding a geodesic by the cutting sequence as it passes a fixed set of curves on M. The latter, Artin method, is the construction using concatenating two sequences, obtained by using a suitable boundary expansion, of two endpoints of a lift of the geodesic (a geodesic in the unit disc). In this thesis, we investigate the more mysterious Artin method for specific examples of surfaces and show that we obtain a sofic system by using Artin method.
Language
English
URI
https://hdl.handle.net/10371/131480
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