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Title: The characterisation of chaos in low dimensional spaces
Author: McCreadie, Geoffrey Alexander
ISNI:       0000 0001 3623 4544
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1983
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This work attempts to characterise some of the complicated behaviour that is observed in many non-linear systems. For example, the frontispiece was generated by iterations of a two dimensional area-preserving mapping (the Chirikov map) that is typical of the systems studied herein. It will be shown that area-preserving deterministic mappings can be accurately characterised by a diffusion constant i.e. a quantity associated with random systems. In addition it shows how perturbation theory has a greater range of validtty than might be expected. The first three chapters introduce a number of physical systems that exhibit this chaotic behaviour and describe useful analytical techniques. Chapter 3 derives a general expression for a diffusion constant for 2D maps of the torus and shows the very good agreement between theory and numerical simulation for two example maps. Chapter 4 shows analytically how this type of deterministic system can be equivalent to a random system without the addition of external noise. Chapters 5 and 6 extend the theory to parameter values where chaos and order coexist and where the dynamics modulate an imposed noise. Chapter 7 calculates the Lyapunov exponent for the one dimensional logistic map. Chapter 8 examines the accuracy of computer models and perturbation schemes via the shadowing property of hyperbolic systems.
Supervisor: Not available Sponsor: Science and Engineering Research Council (Great Britain) ; North Atlantic Treaty Organization ; Université de Genève
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QC Physics