Dynamical System: Circle Maps — Presentation Detail — Celebration of Scholars

Instructions

Student presentations must have a faculty sponsor.

Abstracts must include a title and a description of the research, scholarship, or creative work. The description should be 150-225 words in length and constructed in a format or style appropriate for the presenter’s discipline.

The following points should be addressed within the selected format or style for the abstract:

A clear statement of the problem or question you pursued, or the scholarly goal or creative theme achieved in your work.
A brief comment about the significance or uniqueness of the work.
A clear description of the methods used to achieve the purpose or goals for the work.
A statement of the conclusions, results, outcomes, or recommendations, or if the work is still in progress, the results you expect to report at the event.

Presenter photographs should be head and shoulder shots comparable to passport photos.

Additional Information

More information is available at carthage.edu/celebration-scholars/. The following are members of the Research, Scholarship, and Creativity Committee who are eager to listen to ideas and answer questions:

Jun Wang
Kim Instenes
John Kirk
Nora Nickels
Andrew Pustina
James Ripley

Dynamical System: Circle Maps

Name: Steven Metallo
Major: Mathematics
Hometown: Kenosha
Faculty Sponsor:
Other Sponsors:
Type of research: SURE
Funding: SURE

Abstract

Dynamics is a branch of mathematics that uses function iteration to create a dynamical system. Our focus is on the dynamics of ƒx=2x mod 1, where n is a natural number and the domain is the continuous interval [0,1] where 0≡1. We study this simple function because it leads to complicated dynamics; it has periodic points of every period as well as infinitely many non-periodic points. In order to more efficiently analyze this system, we introduce symbolic dynamics. This is done by using a Markov partition to split up the domain into intervals with specific properties. We apply the intervals of the Markov partition to construct a Markov matrix. Then, for certain Markov partitions, we prove through matrix conjugation that the eigenvalues of the corresponding Markov matrices are 2 and roots of unity.

Poster file