Measuring Complexity in Dynamical Systems Public Deposited

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Last Modified
  • March 19, 2019
Creator
  • 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.
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  • In Copyright
Advisor
  • Mucha, Peter
  • Hawkins, Jane
  • Petersen, Karl Endel
  • Goodman, Sue
  • Marzuola, Jeremy
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2015
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  • Chapel Hill, NC
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