Chaos, Dynamics, and Fractals: An Algorithmic Approach to Deterministic Chaos (Cambridge Nonlinear Science Series, Series Number 2) - Hardcover

McCauley, Joseph L.

Hardcover

ISBN 10: 0521416582 ISBN 13: 9780521416580

Publisher: Cambridge University Press, 1993

Synopsis

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.

About this title

Review

' 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

Book Description

The author presents deterministic chaos from the standpoint of theoretical computer arithmetic, leading to universal properties described by symbolic dynamics.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1993
• Language: English
• ISBN 10: 0521416582
• ISBN 13: 9780521416580
• Binding: Hardcover
• Number of pages: 345