Charts for Prediction and Chance : Dazzling Diagrams on Your PC

by Markus, Mario

• ISBN13: 9781860948350
• ISBN10: 1860948359
• Format: Hardcover
• Copyright: 2008-01-15
• Publisher: World Scientific Pub Co Inc

Summary

Mario Markus is a professor at the University of Dortmund.

Table of Contents

Preface	p. v
Commentary	p. vii
The Useful and the Beautiful	p. 1
The "Objet Trouve" in Mathematics	p. 3
The Mondrian Experiments	p. 5
An Anecdotal Report on Chaos	p. 7
Twenty years ago	p. 7
Vertical pluralism	p. 8
Horizontal pluralism	p. 10
Surprises contrary to reason	p. 11
A Case Submitted to Court	p. 17
Calculation of the "Charts for Prediction and Chance" ([lambda]-Diagrams)	p. 19
The Lyapunov exponent	p. 20
The use of colours and shades of grey	p. 22
Configuration of the diagrams	p. 24
The Significance of Discrete Maps	p. 25
Processes that are inherently discrete in time	p. 25
Data obtained from a continuous process at discrete times	p. 28
Poincare sections	p. 29
Analytical integration	p. 33
Maps with Scientific Applications	p. 37
A kicked electronic oscillator	p. 37
Cardiac oscillations	p. 39
Turbulent diffusion	p. 40
A traffic model	p. 41
The Belousov-Zhabotinsky reaction	p. 42
The international arms race	p. 43
The predictor-corrector equation for the kicked rotator	p. 45
Interdependent economies	p. 46
Asymmetric economic competition	p. 47
Economic-ecological feedback in the fishing business	p. 48
Laser pulse in a ring cavity	p. 49
Periodically driven elements of antiferromagnetic lattices	p. 51
Periodically driven p-n junctions	p. 53
Optical bistability in liquid crystals	p. 53
Host-parasitoid models	p. 54
Other predator-prey models	p. 57
The kicked rotator	p. 59
The buckled beam, Pohl's wheel and Holmes' map	p. 60
Maps of Generic Significance	p. 63
The Gumowski-Mira attractors	p. 63
The logistic equation	p. 65
The discontinuous logistic equation	p. 67
Discontinuity of the slope	p. 69
The KST-map	p. 69
The periodically driven Poincare oscillator	p. 70
The Henon map	p. 71
The Henon-Lozi map	p. 72
The Adams-Bashforth integration procedure	p. 73
Driven linear systems and the Degn-map	p. 74
Chaos via quasiperiodicity	p. 76
A map with an arbitrarily large number of coexisting attractors	p. 79
The Maryland map	p. 80
Riddled and intermingled basins	p. 81
Transition between the tent map and the Bernoulli shift	p. 82
The Kaplan-Yorke map and fractal basin boundaries	p. 85
Chaos control via phase space compression	p. 86
The Mandelbrot set	p. 86
Maps related to strange nonchaotic attractors	p. 88
The sin[superscript 2]-map	p. 92
Discontinuous sin[superscript 2]-maps	p. 92
Other maps	p. 93
Are the [lambda]-Diagrams Fractals?	p. 213
What Can We Learn from [lambda]-Diagrams?	p. 217
Acknowledgments	p. 223
Informal Glossary	p. 225
Abbreviations	p. 227
Instructions for the CD-Rom ([lambda]-Diagrams on Your PC)	p. 229
General information	p. 229
How to run the calculations and specify what exactly to calculate	p. 230
Setting grey levels or colours	p. 234
Blow-ups, rescalings and rotations	p. 236
How to save, load, or exit, and how to create a personal library	p. 237
Fivefold speed with LIB	p. 237
Larger images	p. 239
Bibliography	p. 241
Descriptions of the Colour Plates	p. 249
Colour Plates	p. 253
Index	p. 285
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