Introduction to chaotic dynamical systems
Bernhard, Michael A.
Leader, Jeffery J.
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The emerging discipline known as "chaos theory" is a relatively new field of study with a diverse range of applications (economics, biology, meteorology, etc.). Despite this, there is not as yet a universally accepted definition for "chaos" as it applies to gen- eral dynamical systems. Various approaches range from topological methods of a qualitative description, to physical notions of randomness, information, and entropy in crgodic theory, to the development of computational definitions and algorithms designed to obtain quantitative information. This thesis develops some of the current definitions and discusses several quantita- tive measures of chaos. It is intended to stimulate the interest of undergraduate and graduate students and is accessible to those with a knowledge of advanced calculus and ordinary differential equations. In covering chaos for continuous systems it serves as a complement to the work done by Philip Beaver [Ref. 1], which details chaotic dynamics for discrete systems.
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