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

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

Joseph L. McCauley (Author)

9780521467476, Cambridge University Press

Paperback, published 26 May 1994

348 pages, 77 b/w illus.
22.9 x 15.1 x 1.8 cm, 0.502 kg

'very well written' Journal of the Association of C and C++ Users

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.

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.

Subject Areas: Chaos theory [PBWS], Fractal geometry [PBMX]