Degree Type

Dissertation

Date of Award

2015

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Wolfgang Kliemann

Abstract

In this paper we explore the concept of symbolic dynamical systems whose structure is determined by a directed graph, and then discrete-continuous hybrid systems that arise from such dynamical systems. Typically, symbolic dynamics involve the study of a left shift of a bi-infinite sequence. We examine the case when the bi-infinite system is dictated by a graph; that is, the sequence is a bi-infinite path of a directed graph. We then use the concept to study a system of dynamical systems all on the same compact space M, where "switching" between the systems occurs as given by the bi-infinite sequence in question. The concepts of limit sets, chain recurrent sets, chaos, and Morse sets for these systems are explored.

DOI

https://doi.org/10.31274/etd-180810-3900

Copyright Owner

Kimberly Danielle Ayers

Language

en

File Format

application/pdf

File Size

64 pages

Included in

Mathematics Commons

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