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The characterisation of chaos in low dimensional spaces

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McCreadie, Geoffrey Alexander (1983) The characterisation of chaos in low dimensional spaces. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b1463048~S1

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Abstract

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.

Item Type: Thesis (PhD)
Subjects: Q Science > QC Physics
Library of Congress Subject Headings (LCSH): Chaotic behavior in systems
Official Date: November 1983
Institution: University of Warwick
Theses Department: Department of Physics
Thesis Type: PhD
Publication Status: Unpublished
Supervisor(s)/Advisor: Rowlands, G. (George)
Sponsors: Science and Engineering Research Council (Great Britain) ; North Atlantic Treaty Organization ; Université de Genève
Extent: xiv, 110 leaves
Language: eng

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