| Preface |
|
v | |
| Commentary |
|
vii | |
|
The Useful and the Beautiful |
|
|
1 | (2) |
|
The ``Objet Trouve'' in Mathematics |
|
|
3 | (2) |
|
|
|
5 | (2) |
|
An Anecdotal Report on Chaos |
|
|
7 | (10) |
|
|
|
7 | (1) |
|
|
|
8 | (2) |
|
|
|
10 | (1) |
|
Surprises contrary to reason |
|
|
11 | (6) |
|
A Case Submitted to Court |
|
|
17 | (2) |
|
Calculation of the ``Charts for Prediction and Chance'' (A Diagrams) |
|
|
19 | (6) |
|
|
|
20 | (2) |
|
The use of colours and shades of grey |
|
|
22 | (2) |
|
Configuration of the diagrams |
|
|
24 | (1) |
|
The Significance of Discrete Maps |
|
|
25 | (12) |
|
Processes that are inherently discrete in time |
|
|
25 | (3) |
|
Data obtained from a continuous process at discrete times |
|
|
28 | (1) |
|
|
|
29 | (4) |
|
|
|
33 | (4) |
|
Maps with Scientific Applications |
|
|
37 | (26) |
|
A kicked electronic oscillator |
|
|
37 | (2) |
|
|
|
39 | (1) |
|
|
|
40 | (1) |
|
|
|
41 | (1) |
|
The Belousov-Zhabotinsky reaction |
|
|
42 | (1) |
|
The international arms race |
|
|
43 | (2) |
|
The predictor-corrector equation for the kicked rotator |
|
|
45 | (1) |
|
|
|
46 | (1) |
|
Asymmetric economic competition |
|
|
47 | (1) |
|
Economic-ecological feedback in the fishing business |
|
|
48 | (1) |
|
Laser pulse in a ring cavity |
|
|
49 | (2) |
|
Periodically driven elements of antiferromagnetic lattices |
|
|
51 | (2) |
|
Periodically driven p-n junctions |
|
|
53 | (1) |
|
Optical bistability in liquid crystals |
|
|
53 | (1) |
|
|
|
54 | (3) |
|
Other predator-prey models |
|
|
57 | (2) |
|
|
|
59 | (1) |
|
The buckled beam, Pohl's wheel and Holmes' map |
|
|
60 | (3) |
|
Maps of Generic Significance |
|
|
63 | (150) |
|
The Gumowski-Mira attractors |
|
|
63 | (2) |
|
|
|
65 | (2) |
|
The discontinuous logistic equation |
|
|
67 | (2) |
|
Discontinuity of the slope |
|
|
69 | (1) |
|
|
|
69 | (1) |
|
The periodically driven Poincare oscillator |
|
|
70 | (1) |
|
|
|
71 | (1) |
|
|
|
72 | (1) |
|
The Adams-Bashforth integration procedure |
|
|
73 | (1) |
|
Driven linear systems and the Degn-map |
|
|
74 | (2) |
|
Chaos via quasiperiodicity |
|
|
76 | (3) |
|
A map with an arbitrarily large number of coexisting attractors |
|
|
79 | (1) |
|
|
|
80 | (1) |
|
Riddled and intermingled basins |
|
|
81 | (1) |
|
Transition between the tent map and the Bernoulli shift |
|
|
82 | (3) |
|
The Kaplan-Yorke map and fractal basin boundaries |
|
|
85 | (1) |
|
Chaos control via phase space compression |
|
|
86 | (1) |
|
|
|
86 | (2) |
|
Maps related to strange nonchaotic attractors |
|
|
88 | (4) |
|
|
|
92 | (1) |
|
|
|
92 | (1) |
|
|
|
93 | (120) |
|
Are the λ-Diagrams Fractals? |
|
|
213 | (4) |
|
What Can We Learn from λ-Diagrams? |
|
|
217 | (6) |
|
|
|
223 | (2) |
|
Appendix A Informal Glossary |
|
|
225 | (2) |
|
|
|
227 | (2) |
|
Appendix C Instructions for the CD-Rom (λ-Diagrams on Your PC) |
|
|
229 | (12) |
|
|
|
229 | (1) |
|
How to run the calculations and specify what exactly to calculate |
|
|
230 | (4) |
|
Setting grey levels or colours |
|
|
234 | (2) |
|
Blow-ups, rescalings and rotations |
|
|
236 | (1) |
|
How to save, load, or exit, and how to create a personal library |
|
|
237 | (1) |
|
|
|
237 | (2) |
|
|
|
239 | (2) |
| Bibliography |
|
241 | (8) |
| Descriptions of the Colour Plates |
|
249 | (4) |
| Colour Plates |
|
253 | (32) |
| Index |
|
285 | |
