Chaos: a program collection for the PC
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1994
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 311 S. Ill., graph. Darst. 2 Disketten, 3,5" |
| ISBN: | 3540574573 0387574573 |
Internformat
MARC
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| 100 | 1 | |a Korsch, Hans-Jürgen |d 1944- |e Verfasser |0 (DE-588)123762073 |4 aut | |
| 245 | 1 | 0 | |a Chaos |b a program collection for the PC |c H. J. Korsch ; H.-J. Jodl |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1994 | |
| 300 | |a XIII, 311 S. |b Ill., graph. Darst. |e 2 Disketten, 3,5" | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Chaotic behavior in systems -- Experiments -- Data processing | |
| 650 | 4 | |a Chaotic behavior in systems -- Computer programs | |
| 650 | 4 | |a Digital computer simulation | |
| 650 | 0 | 7 | |a Personal Computer |0 (DE-588)4115533-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Chaostheorie |0 (DE-588)4009754-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineares dynamisches System |0 (DE-588)4126142-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Computersimulation |0 (DE-588)4148259-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Simulation |0 (DE-588)4055072-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Chaotisches System |0 (DE-588)4316104-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4055382-6 |a Software |2 gnd-content | |
| 689 | 0 | 0 | |a Chaotisches System |0 (DE-588)4316104-2 |D s |
| 689 | 0 | 1 | |a Simulation |0 (DE-588)4055072-2 |D s |
| 689 | 0 | 2 | |a Personal Computer |0 (DE-588)4115533-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Chaotisches System |0 (DE-588)4316104-2 |D s |
| 689 | 1 | 1 | |a Computersimulation |0 (DE-588)4148259-1 |D s |
| 689 | 1 | 2 | |a Personal Computer |0 (DE-588)4115533-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Nichtlineares dynamisches System |0 (DE-588)4126142-2 |D s |
| 689 | 2 | 1 | |a Chaostheorie |0 (DE-588)4009754-7 |D s |
| 689 | 2 | 2 | |a Personal Computer |0 (DE-588)4115533-6 |D s |
| 689 | 2 | |5 DE-188 | |
| 689 | 3 | 0 | |a Nichtlineares dynamisches System |0 (DE-588)4126142-2 |D s |
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| 689 | 3 | 2 | |a Computersimulation |0 (DE-588)4148259-1 |D s |
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| 700 | 1 | |a Jodl, Hans-Jörg |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006396573&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006396573 | |
Datensatz im Suchindex
| _version_ | 1807774260979040256 |
|---|---|
| adam_text |
TABLE
OF
CONTENTS
1.
OVERVIEW
AND
BASIC
CONCEPTS
.
1
1.1
INTRODUCTION
.
1
1.2
THE
PROGRAMS
.
5
1.3
LITERATURE
ON
CHAOTIC
DYNAMICS
.
8
2.
NONLINEAR
DYNAMICS
AND
DETERMINISTIC
CHAOS
.
11
2.1
DETERMINISTIC
CHAOS
.
11
2.2
HAMILTONIAN
SYSTEMS
.
12
2.2.1
INTEGRABLE
AND
ERGODIC
SYSTEMS
.
13
2.2.2
POINCARE
SECTIONS
.
16
2.2.3
THE
KAM
THEOREM
.
18
2.2.4
HOMOCLINIC
POINTS
.
20
2.3
DISSIPATIVE
DYNAMICAL
SYSTEMS
.
21
2.3.1
ATTRACTORS
.
23
2.3.2
ROUTES
TO
CHAOS
.
25
2.4
SPECIAL
TOPICS
.
27
2.4.1
THE
POINCARE-BIRKHOFF
THEOREM
.
27
2.4.2
CONTINUED
FRACTIONS
.
29
2.4.3
THE
LYAPUNOV
EXPONENT
.
31
2.4.4
FIXED
POINTS
OF
ONE-DIMENSIONAL
MAPS
.
34
2.4.5
FIXED
POINTS
OF
TWO-DIMENSIONAL
MAPS
.
37
2.4.6
BIFURCATIONS
.
42
REFERENCES
.
43
3.
BILLIARD
SYSTEMS
.
45
3.1
DEFORMATIONS
OF
A
CIRCLE
BILLIARD
.
47
3.2
NUMERICAL
TECHNIQUES
.
51
3.3
INTERACTING
WITH
THE
PROGRAM
.
52
3.4
COMPUTER
EXPERIMENTS
.
56
3.4.1
FROM
REGULARITY
TO
CHAOS
.
56
3.4.2
ZOOMING
IN
.
58
3.4.3
SENSITIVITY
AND
DETERMINISM
.
60
3.4.4
SUGGESTIONS
FOR
ADDITIONAL
EXPERIMENTS
.
61
STABILITY
OF
TWO-BOUNCE
ORBITS
.
61
X
TABLE
OF
CONTENTS
BIFURCATIONS
OF
PERIODIC
ORBITS
.
62
A
NEW
INTEGRABLE
BILLIARD?
.
64
NON-CONVEX
BILLIARDS
.
64
3.5
SUGGESTIONS
FOR
FURTHER
STUDIES
.
64
3.6
REAL
EXPERIMENTS
AND
EMPIRICAL
EVIDENCE
.
65
REFERENCES
.
65
4.
GRAVITATIONAL
BILLIARDS:
THE
WEDGE
.
67
4.1
THE
POINCARE
MAPPING
.
68
4.2
INTERACTING
WITH
THE
PROGRAM
.
73
4.3
COMPUTER
EXPERIMENTS
.
75
4.3.1
PERIODIC
MOTION
AND
PHASE
SPACE
ORGANIZATION
.
75
4.3.2
BIFURCATION
PHENOMENA
.
80
4.3.3
'
PLANE
FILLING
'
WEDGE
BILLIARDS
.
84
4.3.4
SUGGESTIONS
FOR
ADDITIONAL
EXPERIMENTS
.
86
MIXED
A
-
B
ORBITS
.
86
PURE
B
DYNAMICS
.
87
THE
STOCHASTIC
REGION
.
87
BREATHING
CHAOS
.
87
4.4
SUGGESTIONS
FOR
FURTHER
STUDIES
.
87
4.5
REAL
EXPERIMENTS
AND
EMPIRICAL
EVIDENCE
.
88
REFERENCES
.
88
5.
THE
DOUBLE
PENDULUM
.
89
5.1
EQUATIONS
OF
MOTION
.
89
5.2
NUMERICAL
ALGORITHMS
.
91
5.3
INTERACTING
WITH
THE
PROGRAM
.
93
5.4
COMPUTER
EXPERIMENTS
.
98
5.4.1
DIFFERENT
TYPES
OF
MOTION
.
98
5.4.2
DYNAMICS
OF
THE
DOUBLE
PENDULUM
.
103
5.4.3
DESTRUCTION
OF
INVARIANT
CURVES
.
107
5.4.4
SUGGESTIONS
FOR
ADDITIONAL
EXPERIMENTS
.
110
TESTING
THE
NUMERICAL
INTEGRATION
.
110
ZOOMING
IN
.
110
DIFFERENT
PENDULUM
PARAMETERS
.
ILL
5.5
REAL
EXPERIMENTS
AND
EMPIRICAL
EVIDENCE
.
112
REFERENCES
.
114
6.
CHAOTIC
SCATTERING
.
115
6.1
SCATTERING
OFF
THREE
DISKS
.
117
6.2
NUMERICAL
TECHNIQUES
.
121
6.3
INTERACTING
WITH
THE
PROGRAM
.
122
6.4
COMPUTER
EXPERIMENTS
.
124
6.4.1
SCATTERING
FUNCTIONS
AND
TWO-DISK
COLLISIONS
.
124
6.4.2
TREE
ORGANIZATION
OF
THREE-DISK
COLLISIONS
.
127
TABLE
OF
CONTENTS
XI
6.4.3
UNSTABLE
PERIODIC
ORBITS
.
129
6.4.4
FRACTAL
SINGULARITY
STRUCTURE
.
131
6.4.5
SUGGESTIONS
FOR
ADDITIONAL
EXPERIMENTS
.
133
LONG-LIVED
TRAJECTORIES
.
133
INCOMPLETE
SYMBOLIC
DYNAMICS
.
135
MULTISCALE
FRACTALS
.
135
6.5
SUGGESTIONS
FOR
FURTHER
STUDIES
.
135
6.6
REAL
EXPERIMENTS
AND
EMPIRICAL
EVIDENCE
.
135
REFERENCES
.
136
7.
FERMI
ACCELERATION
.
137
7.1
FERMI
MAPPING
.
138
7.2
INTERACTING
WITH
THE
PROGRAM
.
139
7.3
COMPUTER
EXPERIMENTS
.
141
7.3.1
EXPLORING
PHASE
SPACE
FOR
DIFFERENT
WALL
OSCILLATIONS
.
141
7.3.2
KAM
CURVES
AND
STOCHASTIC
ACCELERATION
.
144
7.3.3
FIXED
POINTS
AND
LINEAR
STABILITY
.
147
7.3.4
ABSOLUTE
BARRIERS
.
148
7.3.5
SUGGESTIONS
FOR
ADDITIONAL
EXPERIMENTS
.
150
HIGHER
ORDER
FIXED
POINTS
.
150
STANDARD
MAPPING
.
151
BIFURCATION
PHENOMENA
.
152
INFLUENCE
OF
DIFFERENT
WALL
VELOCITIES
.
153
7.4
SUGGESTIONS
FOR
FURTHER
STUDIES
.
154
7.5
REAL
EXPERIMENTS
AND
EMPIRICAL
EVIDENCE
.
155
REFERENCES
.
155
8.
THE
DUFFING
OSCILLATOR
.
157
8.1
THE
DUFFING
EQUATION
.
157
8.2
NUMERICAL
TECHNIQUES
.
161
8.3
INTERACTING
WITH
THE
PROGRAM
.
161
8.4
COMPUTER
EXPERIMENTS
.
165
8.4.1
CHAOTIC
AND
REGULAR
OSCILLATIONS
.
165
8.4.2
THE
FREE
DUFFING
OSCILLATOR
.
166
8.4.3
ANHARMONIC
VIBRATIONS:
RESONANCES
AND
BISTABILITY.
.
166
8.4.4
COEXISTING
LIMIT
CYCLES
AND
STRANGE
ATTRACTORS
.
170
8.4.5
SUGGESTIONS
FOR
ADDITIONAL
EXPERIMENTS
.
173
HARMONIC
OSCILLATOR
.
173
GRAVITATIONAL
PENDULUM
.
174
EXACT
HARMONIC
RESPONSE
.
174
PERIOD-DOUBLING
BIFURCATIONS
.
175
STRANGE
ATTRACTORS
.
177
8.5
SUGGESTIONS
FOR
FURTHER
STUDIES
.
177
8.6
REAL
EXPERIMENTS
AND
EMPIRICAL
EVIDENCE
.
178
REFERENCES
.
179
XII
TABLE
OF
CONTENTS
9.
FEIGENBAUM
SCENARIO
.
181
9.1
ONE-DIMENSIONAL
MAPS
.
182
9.2
INTERACTING
WITH
THE
PROGRAM
.
184
9.3
COMPUTER
EXPERIMENTS
.
187
9.3.1
PERIOD-DOUBLING
BIFURCATIONS
.
187
9.3.2
THE
CHAOTIC
REGIME
.
191
9.3.3
LYAPUNOV
EXPONENTS
.
194
9.3.4
THE
TENT
MAP
.
196
9.3.5
SUGGESTIONS
FOR
ADDITIONAL
EXPERIMENTS
.
198
DIFFERENT
MAPPING
FUNCTIONS
.
198
PERIODIC
ORBIT
THEORY
.
200
EXPLORING
THE
CIRCLE
MAP
.
202
9.4
SUGGESTIONS
FOR
FURTHER
STUDIES
.
203
9.5
REAL
EXPERIMENTS
AND
EMPIRICAL
EVIDENCE
.
204
REFERENCES
.
205
10.
NONLINEAR
ELECTRONIC
CIRCUITS
.
207
10.1
A
CHAOS
GENERATOR
.
207
10.2
NUMERICAL
TECHNIQUES
.
210
10.3
INTERACTING
WITH
THE
PROGRAM
.
211
10.4
COMPUTER
EXPERIMENTS
.
215
10.4.1
HOPF
BIFURCATION
.
215
10.4.2
PERIOD
DOUBLING
.
217
10.4.3
RETURN
MAP
.
221
10.4.4
SUGGESTIONS
FOR
ADDITIONAL
EXPERIMENTS
.
222
COMPARISON
WITH
AN
ELECTRONIC
CIRCUIT
.
222
DEVIATIONS
FROM
THE
LOGISTIC
MAPPING
.
224
BOUNDARY
CRISIS
.
224
10.5
REAL
EXPERIMENTS
AND
EMPIRICAL
EVIDENCE
.
225
REFERENCES
.
226
11.
MANDELBROT
AND
JULIA
SETS
.
227
11.1
TWO-DIMENSIONAL
ITERATED
MAPS
.
227
11.2
NUMERICAL
AND
COLORING
ALGORITHMS
.
231
11.3
INTERACTING
WITH
THE
PROGRAM
.
233
11.4
COMPUTER
EXPERIMENTS
.
237
11.4.1
MANDELBROT
AND
JULIA
SETS
.
237
11.4.2
ZOOMING
INTO
THE
MANDELBROT
SET
.
240
11.4.3
GENERAL
TWO-DIMENSIONAL
QUADRATIC
MAPPINGS
.
242
11.5
SUGGESTION
FOR
ADDITIONAL
EXPERIMENTS
.
245
COMPONENTS
OF
THE
MANDELBROT
SET
.
245
DISTORTED
MANDELBROT
MAPS
.
245
FURTHER
EXPERIMENTS
.
246
11.6
REAL
EXPERIMENTS
AND
EMPIRICAL
EVIDENCE
.
247
REFERENCES
.
247
TABLE
OF
CONTENTS
XIII
12.
ORDINARY
DIFFERENTIAL
EQUATIONS
.
249
12.1
NUMERICAL
TECHNIQUES
.
250
12.2
INTERACTING
WITH
THE
PROGRAM
.
250
12.3
COMPUTER
EXPERIMENTS
.
255
12.3.1
THE
PENDULUM
.
255
12.3.2
A
SIMPLE
HOPF
BIFURCATION
.
257
12.3.3
THE
DUFFING
OSCILLATOR
REVISITED
.
260
12.3.4
HILL
'
S
EQUATION
.
263
12.3.5
THE
LORENZ
ATTRACTOR
.
270
12.3.6
THE
ROSSLER
ATTRACTOR
.
274
12.3.7
THE
HENON-HEILES
SYSTEM
.
275
12.3.8
SUGGESTIONS
FOR
ADDITIONAL
EXPERIMENTS
.
279
LORENZ
SYSTEM:
LIMIT
CYCLES
AND
INTERMITTENCY
.
279
THE
RESTRICTED
THREE
BODY
PROBLEM
.
280
12.4
SUGGESTIONS
FOR
FURTHER
STUDIES
.
284
REFERENCES
.
289
A.
SYSTEM
REQUIREMENTS
AND
PROGRAM
INSTALLATION
.
291
A.L
SYSTEM
REQUIREMENTS
.
291
A.2
INSTALLING
THE
PROGRAMS
.
292
A.
3
PROGRAMS
AND
FILES
.
292
B.
GENERAL
REMARKS
ON
USING
THE
PROGRAMS
.
295
B.L
MASK
MENUS
.
295
B.2
THE
FILE-SELECT
BOX
.
296
B.3
INPUT
OF
MATHEMATICAL
EXPRESSIONS
.
297
B.4
SELECTION
OF
POINTS
OR
AREAS
IN
GRAPHICS
.
298
GLOSSARY
.
299
SUBJECT
INDEX
.
307 |
| any_adam_object | 1 |
| author | Korsch, Hans-Jürgen 1944- Jodl, Hans-Jörg |
| author_GND | (DE-588)123762073 |
| author_facet | Korsch, Hans-Jürgen 1944- Jodl, Hans-Jörg |
| author_role | aut aut |
| author_sort | Korsch, Hans-Jürgen 1944- |
| author_variant | h j k hjk h j j hjj |
| building | Verbundindex |
| bvnumber | BV009671428 |
| callnumber-first | Q - Science |
| callnumber-label | Q172 |
| callnumber-raw | Q172.5.C45K67 1994 |
| callnumber-search | Q172.5.C45K67 1994 |
| callnumber-sort | Q 3172.5 C45 K67 41994 |
| callnumber-subject | Q - General Science |
| classification_rvk | ST 630 UG 3900 |
| classification_tum | DAT 780f MAT 587f DAT 532f |
| ctrlnum | (OCoLC)632374234 (DE-599)BVBBV009671428 |
| dewey-full | 530.1/0118520 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/01185 20 |
| dewey-search | 530.1/01185 20 |
| dewey-sort | 3530.1 41185 220 |
| dewey-tens | 530 - Physics |
| discipline | Physik Informatik Mathematik |
| format | Book |
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| genre | (DE-588)4055382-6 Software gnd-content |
| genre_facet | Software |
| id | DE-604.BV009671428 |
| illustrated | Illustrated |
| indexdate | 2024-08-19T00:38:00Z |
| institution | BVB |
| isbn | 3540574573 0387574573 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006396573 |
| oclc_num | 632374234 |
| open_access_boolean | |
| owner | DE-20 DE-92 DE-703 DE-29T DE-91G DE-BY-TUM DE-83 DE-188 |
| owner_facet | DE-20 DE-92 DE-703 DE-29T DE-91G DE-BY-TUM DE-83 DE-188 |
| physical | XIII, 311 S. Ill., graph. Darst. 2 Disketten, 3,5" |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| spelling | Korsch, Hans-Jürgen 1944- Verfasser (DE-588)123762073 aut Chaos a program collection for the PC H. J. Korsch ; H.-J. Jodl Berlin [u.a.] Springer 1994 XIII, 311 S. Ill., graph. Darst. 2 Disketten, 3,5" txt rdacontent n rdamedia nc rdacarrier Datenverarbeitung Chaotic behavior in systems -- Experiments -- Data processing Chaotic behavior in systems -- Computer programs Digital computer simulation Personal Computer (DE-588)4115533-6 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf (DE-588)4055382-6 Software gnd-content Chaotisches System (DE-588)4316104-2 s Simulation (DE-588)4055072-2 s Personal Computer (DE-588)4115533-6 s DE-604 Computersimulation (DE-588)4148259-1 s Nichtlineares dynamisches System (DE-588)4126142-2 s Chaostheorie (DE-588)4009754-7 s DE-188 1\p DE-604 Jodl, Hans-Jörg Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006396573&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Korsch, Hans-Jürgen 1944- Jodl, Hans-Jörg Chaos a program collection for the PC Datenverarbeitung Chaotic behavior in systems -- Experiments -- Data processing Chaotic behavior in systems -- Computer programs Digital computer simulation Personal Computer (DE-588)4115533-6 gnd Chaostheorie (DE-588)4009754-7 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Computersimulation (DE-588)4148259-1 gnd Simulation (DE-588)4055072-2 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4115533-6 (DE-588)4009754-7 (DE-588)4126142-2 (DE-588)4148259-1 (DE-588)4055072-2 (DE-588)4316104-2 (DE-588)4055382-6 |
| title | Chaos a program collection for the PC |
| title_auth | Chaos a program collection for the PC |
| title_exact_search | Chaos a program collection for the PC |
| title_full | Chaos a program collection for the PC H. J. Korsch ; H.-J. Jodl |
| title_fullStr | Chaos a program collection for the PC H. J. Korsch ; H.-J. Jodl |
| title_full_unstemmed | Chaos a program collection for the PC H. J. Korsch ; H.-J. Jodl |
| title_short | Chaos |
| title_sort | chaos a program collection for the pc |
| title_sub | a program collection for the PC |
| topic | Datenverarbeitung Chaotic behavior in systems -- Experiments -- Data processing Chaotic behavior in systems -- Computer programs Digital computer simulation Personal Computer (DE-588)4115533-6 gnd Chaostheorie (DE-588)4009754-7 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Computersimulation (DE-588)4148259-1 gnd Simulation (DE-588)4055072-2 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Datenverarbeitung Chaotic behavior in systems -- Experiments -- Data processing Chaotic behavior in systems -- Computer programs Digital computer simulation Personal Computer Chaostheorie Nichtlineares dynamisches System Computersimulation Simulation Chaotisches System Software |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006396573&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT korschhansjurgen chaosaprogramcollectionforthepc AT jodlhansjorg chaosaprogramcollectionforthepc |