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

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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Publication Status:	Unpublished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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