Measuring Complexity in Dynamical Systems Public Deposited
- Last Modified
- March 19, 2019
- Creator
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Wilson, Benjamin
- Affiliation: College of Arts and Sciences, Department of Mathematics
- Abstract
- Measuring the complexity of dynamical systems is important in order to classify them and better understand them. In 1958 Kolmogorov introduced to ergodic theory an analogue of Shannon's information-theoretic entropy as a measure of disorder or uncertainty in a system. Based on this concept and ideas from neuroscience and information theory, we define the intricacy and average sample complexity of a topological dynamical system and a measure-preserving dynamical system. We examine these new complexity measurements in both the topological and measure-theoretic settings, including analysis of symbolic dynamical systems and Markov shifts. We compare these measurements to the usual measure-theoretic and topological entropies, give some properties of these quantities, and look at some questions that they raise.
- Date of publication
- May 2015
- Keyword
- Subject
- DOI
- Identifier
- Resource type
- Rights statement
- In Copyright
- Advisor
- Marzuola, Jeremy
- Hawkins, Jane
- Goodman, Sue
- Mucha, Peter
- Petersen, Karl Endel
- Degree
- Doctor of Philosophy
- Degree granting institution
- University of North Carolina at Chapel Hill Graduate School
- Graduation year
- 2015
- Language
- Publisher
- Place of publication
- Chapel Hill, NC
- Access
- There are no restrictions to this item.
- Parents:
This work has no parents.
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