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Publication Date

2022-05-09

First Advisor

Geremias Polanco

Document Type

Honors Project

Degree Name

Bachelor of Arts

Department

Mathematics and Statistics

Keywords

mathematics, continued fraction, dynamical system, number theory, sequence

Abstract

In this thesis, we study number theoretic properties of special orbits generated

by a discrete dynamical system with countable number of discontinuities. The

function generating the system is related to a variant of the Minimum Excluded

Algorithm in connection to Beatty sequences, and also to transformations used for

finding substitution invariant Sturmian words. We show that these orbits are nested

in the following sense: orbits generated by larger seed contains orbits of smaller

seeds. Moreover, these orbits stabilize at 1, and also have symmetry, self-similarity

structure, and quasi-periodicity. In the process, we found interesting connections

to continued fractions.

Rights

©2022 Pham Dam Anh Nguyen. Access limited to the Smith College community and other researchers while on campus. Smith College community members also may access from off-campus using a Smith College log-in. Other off-campus researchers may request a copy through Interlibrary Loan for personal use.

Language

English

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