Chaos, Dynamics, and Fractals: An Algorithmic Approach to Deterministic Chaos (Cambridge Nonlinear Science Series)
Cambridge University Press
Edition: New Ed, 1/5/2010
EAN 9780521467476, ISBN10: 0521467470
Paperback, 348 pages, 22.9 x 15.2 x 2.2 cm
Language: English
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.
' a very readable account ... an excellent introduction to fractals and deterministic chaos ...' Chemistry in Britain