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Chaos, Dynamics, and Fractals: An Algorithmic Approach to Deterministic Chaos

Joseph L. McCauley (University of Houston)

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Cambridge University Press
25 July 1994
Differential calculus & equations; Chaos theory
This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.
By:   Joseph L. McCauley (University of Houston)
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Volume:   2
Dimensions:   Height: 229mm,  Width: 152mm,  Spine: 20mm
Weight:   510g
ISBN:   9780521467476
ISBN 10:   0521467470
Series:   Cambridge Nonlinear Science Series
Pages:   348
Publication Date:   25 July 1994
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
Foreword; Introduction; 1. Flows in phase space; 2. Introduction to deterministic chaos; 3. Conservative synamical systems; 4. Fractals and fragmentation in phase space; 5. The way to chaos by instability of quasiperiodic orbits; 6. The way to chaos by period doubling; 7. Multifractals; 8. Statistical physics on chaotic symbol sequences; 9. Universal chaotic dynamics; 10. Intermittence in fluid dynamics; 11. From flows to automata: chaotic systems as completely deterministic machines; References; Index.

Reviews for Chaos, Dynamics, and Fractals: An Algorithmic Approach to Deterministic Chaos

' a very readable account ... an excellent introduction to fractals and deterministic chaos ...' Chemistry in Britain 'very well written' Journal of the Association of C and C++ Users


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