Geodesic Flow of the Modular Surface and Continued Fractions

de Pooter, Jacobus Sander (2019) Geodesic Flow of the Modular Surface and Continued Fractions. Bachelor's Thesis, Mathematics.

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Abstract

The study of geodesic flows on hyperbolic surfaces has a long and rich history. One of the reasons for its rise to the spotlight is that it provides a deep and fascinating link across multiple areas of mathematics, such as dynamical systems, spectral theory, geometry and number theory, and of physics, such as thermodynamics and quantum mechanics. In this thesis we will focus on the relation between the geodesic flow on the modular surface, a particular example of hyperbolic surfaces, and the Gauss map. We will exploit this relation to transfer results from different mathematical realms and establish some of the interdisciplinary connections mentioned above. The main investigative method will be a literature study: we will use a selection of articles, textbooks, monographs and lecture material to depict a coherent explanation of some of the theories involved and their relations.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Seri, M.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	12 Jul 2019
Last Modified:	17 Jul 2019 09:59
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/20174

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