Chaos: the science of predictable random motion
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2011
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIII, 369 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 9780199594573 9780199594580 |
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| 245 | 1 | 0 | |a Chaos |b the science of predictable random motion |c Richard Kautz |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2011 | |
| 300 | |a XIII, 369 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Prediction theory | |
| 650 | 4 | |a Chaotic behavior in systems | |
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Record in the Search Index
| _version_ | 1804143424496992256 |
|---|---|
| adam_text | Contents
I Introduction
1
Chaos everywhere
3
1.1
Tilt-A-Whirl
4
1.2
Digits of
7Г
6
1.3
Butterfly effect
9
1.4
Weather prediction
12
1.5
Inward spiral
13
Further reading
15
II Dynamics
17
2
Galileo Galilei
—
Birth of a new science
19
2.1
When will we get there?
20
2.2
Computer animation
21
2.3
Acceleration
23
2.4
Free-fall
24
2.5
Reconstructing the past
27
2.6
Projectile motion
28
Further reading
30
3
Isaac Newton
—
Dynamics perfected
32
3.1
Equations of motion
33
3.2
Force laws
34
3.3
Calculus
38
Further reading
42
4
Celestial mechanics
—
The clockwork universe
43
4.1
Ptolemy
43
4.2
Copernicus
44
4.3
Brahe
and Kepler
47
4.4
Universal gravitation
49
4.5
Circular orbits
50
4.6
Elliptical orbits
53
4.7
Clockwork universe
56
Further reading
58
χ
Contents
5
The pendulum
—
Linear and nonlinear
60
5.1
Rotational motion
61
5.2
Torque
62
5.3
Pendulum dynamics
64
5.4
Quality factor
67
5.5
Pendulum clock
69
5.6
Frequency
72
5.7
Nonlinearity
73
5.8
Where s the chaos?
74
Further reading
75
6
Sychronization
—
The
Josephson
effect
77
6.1
Hysteresis
78
6.2
Multistability
80
6.3
Synchronization
82
6.4
Symmetry breaking
85
6.5
Josephson
voltage standard
87
Further reading
90
III Random motion
93
7
Chaos forgets the past
95
7.1
Period doubling
97
7.2
Random rotation
99
7.3
Statistics
102
7.4
Correlation 105
7.5
Voltage-standard redux
Ю9
Further reading H2
8
Chaos takes a random walk
ПЗ
8.1
Probability
114
8.2
Quincunx
117
8.3
Pascal s triangle
И9
8.4
Diffusion
121
8.5
Chaotic walk
124
8.6
In search of true randomness
125
Further reading
126
9
Chaos makes noise
128
9.1
Beethoven s Fifth I28
9.2
Fourier
131
9.3
Frequency analysis
133
9.4
Music to the ear
137
9.5
White noise
138
9.6
Random or correlated?
141
Further reading
142
Contents xi
10 Edward Lorenz—
Butterfly
effect
10.1
Lorenz
equations
10.2
Exponential growth
10.3
Exponential and logarithmic functions
10.4
Liapunov exponent
10.5
Exponential decay
10.6
Weather prediction
Further reading
11
Chaos comes of age
11.1
Kinds of chaos
11.2
Maxwell
11.3
Poincarć
11.4
Hadamard
11.5
Borei
11.6
Birkhoff
11.7
Chaos sleeps
11.8
Golden age of chaos
11.9
Ueda
IV Sensitive motion
143
145
146
150
153
155
158
160
164
165
165
166
167
168
170
172
172
174
175
11.10
What took so long?
176
Further reading
178
12
Tilt
-А-
Whirl
—
Chaos at the amusement park
180
12.1
Selmer
181
12.2
Mathematical model
183
186
189
190
192
196
199
200
201
203
206
208
211
214
217
220
222
Further reading
223
12.3
Dynamics
12.4
Liapunov exponent
12.5
Computational limit
12.6
Environmental perturbation
12.7
Long-lived chaotic transients
Further reading
13
Billiard-ball chaos
—
Atomic disorder
13.1
Joule and energy
13.2
Carnot and reversibility
13.3
Clausius and entropy
13.4
Kinetic theory of gases
13.5
Boltzmann and entropy
13.6
Chaos and ergodicity
13.7
Stadium billiards
13.8
Time s arrow
13.9
Atomic hypothesis
xii Contents
14
Iterated maps
—
Chaos made simple
225
14.1
Simple chaos
226
14.2
Liapunov exponent
230
14.3
Stretching and folding
234
14.4
Ulam
and
von
Neumann
—
Random numbers
234
14.5
Chaos explodes
237
14.6
Shift map—Bare chaos
239
14.7
Origin of randomness
242
14.8
Mathemagic
245
Further reading
248
V Topology of motion
251
253
255
257
259
260
261
264
267
268
16
Strange attractor
270
16.1
Poincaré
section
271
16.2
Saddle orbit
274
278
278
281
283
285
286
286
288
290
293
294
297
18
Stephen
Smale
—
Horseshoe map
298
18.1
Horseshoe map
298
18.2
Invariant set
301
18.3
Symbolic dynamics
304
15
State space
—
Going with the flow
15.1
State space
15.2
Attracting point
15.3
Contracting flow
15.4
Basin of attraction
15.5
Saddle
15.6
Limit cycle
15.7
Poincaré—
Bendixson theorem
Further reading
16.3
Period doubling
16.4
Strange attractor
16.5
Chaotic flow
16.6
Stretching and folding
Further reading
17
Fractal geometry
17.1
Mathematical monster
17.2
Hausdorff
—
Fractal dimension
17.3
Mandelbrot
—
Fractal defined
17.4
Physical fractals
17.5
Fractal attractor
Further readins
18.4 3-D
flow
18.5
Structural stability
18.6
Protests and prizes
Further reading
19
Henri
Poincaré
—
Topological tangle
19.1
Homoclinic point
19.2
Homoclinic trajectory
19.3
Homoclinic tangle
19.4
Fixed-point theorem
19.5
Horseshoe
19.6
Poincaré-Birkhoff Smale
theorem
19.7
Heteroclinic tangle
19.8
Fractal basin boundary
19.9
Robust chaos
19.10
Paradox lost
19.11
Stability of the Solar System
Further reading
VI Conclusion
20
Chaos goes to work
20.1
Randomness
20.2
Prediction
20.3
Suppressing chaos
20.4
Hitchhiker s guide to state space
20.5
Space travel
20.6
Weather modification
20.7
Adaptation
20.8
Terra incognita
Further reading
Bibliography
Index
Contents
xiii
307
308
308
310
312
313
315
318
320
321
322
325
326
329
330
332
333
335
337
337
338
341
345
348
351
353
357
358
359
367
Based on only elementary mathematics, this engaging
account of chaos theory bridges the gap between
introductions for the layman and college-level texts.
It develops the science of dynamic
s
in terms of small
time steps, describes the phenomenon of chaos
through simple examples, and concludes with a
close look at a homoclinic tangle, the mathematical
monster at the heart of chaos. The presentation is
enhanced by many figures, animations of chaotic
motion (available on a companion CD), and
biographical sketches of the pioneers of dynamics
and chaos theory. To ensure accessibility to motivated
high school students, care has been taken to explain
advanced mathematical concepts simply, including
exponentials and logarithms, probability, correlation,
frequency analysis, fractals, and
transfinite
numbers.
These tools helj) to resolve the intriguing paradox of
motion that is predictable and yet random, while the
final chapter explores the various ways chaos theory
has been put to practical use.
Richard Kautz
formerly of the National Institute
d
Technology, Boulder, Colorado.
Dr. Kautz has written a book that captures the essentials
oí
ι
haos
in a quantitative wav but without advanced
mathematics. It is highlv recommended lor students and
others with a good background in algebra and trigonometry
and with a desire tor a better understanding of the
Julien
Clinton Sprott, University
ofiľisconsm,
Madison
The writing style is engaging and readable
. . .
while their
is a great deal of mathematical detail in the book, it is
introduced careiullv and thoroughly. Having
a
Dynamica
Lab of computational examples is an excellent notion,
Rob Sturman. University of Leeds
Kautz s Chaos provide
many aspects of nonlin
tales about the pendult
quincunx, the first foul
ny, theTilt-A-Whirl and homocli
algebra geomí>frv
лпґі
trionnnmi
Robert
С.
Hilborn, University oJTexas at Dallas
ALSO PUBLISHED
OXFORD UNIVERSITY PRESS:
The Pendulum
Chaos and Nonlinear Dynamics
From Cosmos to Chaos
Quantum Physics
A Zeptospace
Ody
OXPORD
Cover image:
(1)
The Great Wave oft Kamga*
Katsushika
H irtesv
of the
Librarii-
of Congress.
(2)
The
fractal geometr
ot chaotic
motion as revealed by
a stroboscopie
recording of a driven pendulum.
ISBN
978-0-19-959458-0
www.oup.com
|
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| id | DE-604.BV036758182 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:47:27Z |
| institution | BVB |
| isbn | 9780199594573 9780199594580 |
| language | English |
| lccn | 2010030953 |
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| physical | XIII, 369 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Kautz, Richard Verfasser (DE-588)142972134 aut Chaos the science of predictable random motion Richard Kautz 1. publ. Oxford [u.a.] Oxford Univ. Press 2011 XIII, 369 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Prediction theory Chaotic behavior in systems Chaotisches System (DE-588)4316104-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020675299&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020675299&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kautz, Richard Chaos the science of predictable random motion Prediction theory Chaotic behavior in systems Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4316104-2 |
| title | Chaos the science of predictable random motion |
| title_auth | Chaos the science of predictable random motion |
| title_exact_search | Chaos the science of predictable random motion |
| title_full | Chaos the science of predictable random motion Richard Kautz |
| title_fullStr | Chaos the science of predictable random motion Richard Kautz |
| title_full_unstemmed | Chaos the science of predictable random motion Richard Kautz |
| title_short | Chaos |
| title_sort | chaos the science of predictable random motion |
| title_sub | the science of predictable random motion |
| topic | Prediction theory Chaotic behavior in systems Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Prediction theory Chaotic behavior in systems Chaotisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020675299&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020675299&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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