Measuring Complexity in Dynamical Systems

Measuring Complexity in Dynamical Systems Public Deposited

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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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