Chaos : a program collection for the PC

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010184919	Q172.5.C45 K67 2007	Open Access Book	Book	Searching... Unknown
Searching... PSZ JB	30000003490186	Q172.5.C45 K67 2007	Open Access Book	Book	Searching... Unknown

Ithasbeenthirteenyearssincetheappearanceofthe?rsteditionofthisbook, and nine years after the second. Meanwhile, chaotic (or nonlinear) dynamics is established as an essential part of courses in physics and it still fascinates students, scientists and even nonacademic people, in particular because of the beauty of computer generated images appearing frequently in this ?eld. Quite generally, computers are an ideal tool for exploring and demonstr- ing the intricate features of chaotic dynamics. The programs in the previous editions of this book have been designed to support such studies even for the non-experienced users of personal computers. However, caused by the rapid development of the computational world, these programs written in Turbo Pascal appeared in an old-fashioned design compared to the up-to-date st- dard.Evenmoreimportant,thoseprogramswouldnotproperlyoperateunder recent versions of the Windows operating system. In addition, there is an - creasing use of Linux operating systems. Therefore, for the present edition, all the programs have been entirely rewritten in C++ and, of course, revised and polished. Two version of the program codes are supplied working under Windows or Linux operating systems. We have again corrected a few passage in the text of the book and added somemorerecentdevelopmentsinthe?eldofchaoticdynamics.Finallyanew program treating the important class of two-dimensional discrete ('kicked') systems has been added and described in Chap.13.

Reviews 1

Choice Review

Readers with a foundation in the fundamental relations and mathematics of chaos can use this revised edition (2nd ed., 1998) to develop the skills necessary to apply chaos theory to emerging areas of study. Best thought of as a second course in chaos, the work's strength lies in its blending of theory, experiment, and computer simulation. This reviewer feels that this is clearly the way to learn chaos. By working through computer simulations and real experiments while learning the theory, users can easily see how the theory functions and is applied. Korsch and colleagues (all, Universitat Regensburg, Germany) address a different topic in each chapter, including collisions in systems, the double pendulum, chaotic scattering, Fermi mapping, the Duffing oscillator, Feigenbaum maps, electronic circuits, Mandelbrot and Julia sets, ordinary differential equations, and kicked systems. Even with the accompanying CD-ROM, the text is well illustrated and gives good explanations on using the programs (written in C++ in both Windows and Linux versions). Summing Up: Recommended. Upper-division undergraduates through researchers/faculty. E. Kincanon Gonzaga University

1 Overview and Basic Concepts	p. 1
1.1 Introduction	p. 1
1.2 The Programs	p. 5
1.3 Literature on Chaotic Dynamics	p. 8
2 Nonlinear Dynamics and Deterministic Chaos	p. 11
2.1 Deterministic Chaos	p. 12
2.2 Hamiltonian Systems	p. 13
2.2.1 Integrable and Ergodic Systems	p. 13
2.2.2 Poincare Sections	p. 16
2.2.3 The KAM Theorem	p. 18
2.2.4 Homoclinic Points	p. 20
2.3 Dissipative Dynamical Systems	p. 22
2.3.1 Attractors	p. 24
2.3.2 Routes to Chaos	p. 26
2.4 Special Topics	p. 27
2.4.1 The Poincare-Birkhoff Theorem	p. 28
2.4.2 Continued Fractions	p. 29
2.4.3 The Lyapunov Exponent	p. 32
2.4.4 Fixed Points of One-Dimensional Maps	p. 35
2.4.5 Fixed Points of Two-Dimensional Maps	p. 38
2.4.6 Bifurcations	p. 44
References	p. 45
3 Billiard Systems	p. 47
3.1 Deformations of a Circle Billiard	p. 50
3.2 Numerical Techniques	p. 53
3.3 Interacting with the Program	p. 54
3.4 Computer Experiments	p. 58
3.4.1 From Regularity to Chaos	p. 58
3.4.2 Zooming In	p. 60
3.4.3 Sensitivity and Determinism	p. 61
3.4.4 Suggestions for Additional Experiments	p. 63
3.5 Suggestions for Further Studies	p. 66
3.6 Real Experiments and Empirical Evidence	p. 66
References	p. 67
4 Gravitational Billiards: The Wedge	p. 69
4.1 The Poincare Mapping	p. 70
4.2 Interacting with the Program	p. 75
4.3 Computer Experiments	p. 77
4.3.1 Periodic Motion and Phase Space Organization	p. 77
4.3.2 Bifurcation Phenomena	p. 81
4.3.3 'Plane Filling' Wedge Billiards	p. 86
4.3.4 Suggestions for Additional Experiments	p. 88
4.4 Suggestions for Further Studies	p. 89
4.5 Real Experiments and Empirical Evidence	p. 90
References	p. 90
5 The Double Pendulum	p. 91
5.1 Equations of Motion	p. 91
5.2 Numerical Algorithms	p. 93
5.3 Interacting with the Program	p. 93
5.4 Computer Experiments	p. 98
5.4.1 Different Types of Motion	p. 98
5.4.2 Dynamics of the Double Pendulum	p. 102
5.4.3 Destruction of Invariant Curves	p. 107
5.4.4 Suggestions for Additional Experiments	p. 110
5.5 Real Experiments and Empirical Evidence	p. 111
References	p. 113
6 Chaotic Scattering	p. 115
6.1 Scattering off Three Disks	p. 117
6.2 Numerical Techniques	p. 121
6.3 Interacting with the Program	p. 121
6.4 Computer Experiments	p. 124
6.4.1 Scattering Functions and Two-Disk Collisions	p. 124
6.4.2 Tree Organization of Three-Disk Collisions	p. 127
6.4.3 Unstable Periodic Orbits	p. 129
6.4.4 Fractal Singularity Structure	p. 131
6.4.5 Suggestions for Additional Experiments	p. 133
6.5 Suggestions for Further Studies	p. 135
6.6 Real Experiments and Empirical Evidence	p. 136
References	p. 136
7 Fermi Acceleration	p. 137
7.1 Fermi Mapping	p. 138
7.2 Interacting with the Program	p. 139
7.3 Computer Experiments	p. 142
7.3.1 Exploring Phase Space for Different Wall Oscillations	p. 142
7.3.2 KAM Curves and Stochastic Acceleration	p. 144
7.3.3 Fixed Points and Linear Stability	p. 146
7.3.4 Absolute Barriers	p. 148
7.3.5 Suggestions for Additional Experiments	p. 150
7.4 Suggestions for Further Studies	p. 154
7.5 Real Experiments and Empirical Evidence	p. 154
References	p. 155
8 The Duffing Oscillator	p. 157
8.1 The Duffing Equation	p. 157
8.2 Numerical Techniques	p. 161
8.3 Interacting with the Program	p. 161
8.4 Computer Experiments	p. 168
8.4.1 Chaotic and Regular Oscillations	p. 168
8.4.2 The Free Duffing Oscillator	p. 168
8.4.3 Anharmonic Vibrations: Resonances and Bistability	p. 171
8.4.4 Coexisting Limit Cycles and Strange Attractors	p. 174
8.4.5 Suggestions for Additional Experiments	p. 176
8.5 Suggestions for Further Studies	p. 181
8.6 Real Experiments and Empirical Evidence	p. 181
References	p. 183
9 Feigenbaum Scenario	p. 185
9.1 One-Dimensional Maps	p. 186
9.2 Interacting with the Program	p. 188
9.3 Computer Experiments	p. 191
9.3.1 Period-Doubling Bifurcations	p. 191
9.3.2 The Chaotic Regime	p. 195
9.3.3 Lyapunov Exponents	p. 199
9.3.4 The Tent Map	p. 200
9.3.5 Suggestions for Additional Experiments	p. 202
9.4 Suggestions for Further Studies	p. 206
9.5 Real Experiments and Empirical Evidence	p. 208
References	p. 209
10 Nonlinear Electronic Circuits	p. 211
10.1 A Chaos Generator	p. 211
10.2 Numerical Techniques	p. 214
10.3 Interacting with the Program	p. 215
10.4 Computer Experiments	p. 220
10.4.1 Hopf Bifurcation	p. 220
10.4.2 Period-Doubling	p. 221
10.4.3 Return Map	p. 225
10.4.4 Suggestions for Additional Experiments	p. 226
10.5 Real Experiments and Empirical Evidence	p. 229
References	p. 230
11 Mandelbrot and Julia Sets	p. 231
11.1 Two-Dimensional Iterated Maps	p. 231
11.2 Numerical Methods	p. 235
11.3 Interacting with the Program	p. 236
11.4 Computer Experiments	p. 242
11.4.1 Mandelbrot and Julia-sets	p. 242
11.4.2 Zooming into the Mandelbrot Set	p. 244
11.4.3 General Two-Dimensional Quadratic Mappings	p. 245
11.4.4 Suggestions for Additional Experiments	p. 249
11.5 Suggestions for Further Studies	p. 251
11.6 Real Experiments and Empirical Evidence	p. 252
References	p. 253
12 Ordinary Differential Equations	p. 255
12.1 Numerical Techniques	p. 256
12.2 Interacting with the Program	p. 256
12.3 Computer Experiments	p. 268
12.3.1 The Pendulum	p. 268
12.3.2 A Simple Hopf Bifurcation	p. 270
12.3.3 The Duffing Oscillator Revisited	p. 273
12.3.4 Hill's Equation	p. 275
12.3.5 The Lorenz Attractor	p. 281
12.3.6 The Rossler Attractor	p. 284
12.3.7 The Henon-Heiles System	p. 285
12.3.8 Suggestions for Additional Experiments	p. 288
12.4 Suggestions for Further Studies	p. 293
References	p. 298
13 Kicked Systems	p. 301
13.1 Interacting with the Program	p. 303
13.2 Computer Experiments	p. 307
13.2.1 The Standard Mapping	p. 307
13.2.2 The Kicked Quartic Oscillator	p. 309
13.2.3 The Kicked Quartic Oscillator with Damping	p. 311
13.2.4 The Henon Map	p. 312
13.2.5 Suggestions for Additional Experiments	p. 313
13.3 Real Experiments and Empirical Evidence	p. 316
References	p. 316
A System Requirements and Program Installation	p. 319
A.1 System Requirements	p. 319
A.2 Installing the Programs	p. 319
A.2.1 Windows Operating System	p. 320
A.2.2 Linux Operating System	p. 320
A.3 Programs	p. 321
A.4 Third Party Software	p. 321
B General Remarks on Using the Programs	p. 323
B.1 Interaction with the Programs	p. 323
B.2 Input of Mathematical Expressions	p. 325
Glossary	p. 327
Index	p. 335

Available:*

On Order

Summary

Summary

Reviews 1

Choice Review

Table of Contents