Introduction to applied nonlinear dynamical systems and chaos:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York [u.a.]
Springer
1996
|
| Ausgabe: | 4. print. |
| Schriftenreihe: | Texts in applied mathematics
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 651 - 666 |
| Beschreibung: | XIV, 672 S. graph. Darst. |
| ISBN: | 3540970037 0387970037 |
Internformat
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| 100 | 1 | |a Wiggins, Stephen |d ca. 20./21. Jh. |e Verfasser |0 (DE-588)1247764664 |4 aut | |
| 245 | 1 | 0 | |a Introduction to applied nonlinear dynamical systems and chaos |c Stephen Wiggins |
| 250 | |a 4. print. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a XIV, 672 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Texts in applied mathematics |v 2 | |
| 500 | |a Literaturverz. S. 651 - 666 | ||
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 0 | 7 | |a Nichtlineare Theorie |0 (DE-588)4251279-7 |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 Differenzierbares dynamisches System |0 (DE-588)4137931-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Chaos |0 (DE-588)4191419-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1805067796078395392 |
|---|---|
| adam_text |
CONTENTS
SERIES
PREFACE
VII
PREFACE
IX
0
INTRODUCTION
1
1
THE
GEOMETRICAL
POINT
OF
VIEW
OF
DYNAMICAL
SYSTEMS:
BACKGROUND
MATERIAL,
POINCARE
MAPS,
AND
EXAMPLES
5
1.1
BACKGROUND
MATERIAL
FROM
DYNAMICAL
SYSTEMS
THEORY
6
1.1
A
EQUILIBRIUM
SOLUTIONS:
LINEARIZED
STABILITY
6
1.1
B
LIAPUNOV
FUNCTIONS
10
1.1C
INVARIANT
MANIFOLDS:
LINEAR
AND
NONLINEAR
SYSTEMS
14
1.1D
PERIODIC
SOLUTIONS
25
1.1E
INTEGRABLE
VECTOR
FIELDS
ON
TWO-MANIFOLDS
28
I.I
F
INDEX
THEORY
35
1.1G
SOME
GENERAL
PROPERTIES
OF
VECTOR
FIELDS:
EXISTENCE,
UNIQUENESS,
DIFFERENTIABILITY,
AND
FLOWS
36
1.1H
ASYMPTOTIC
BEHAVIOR
41
L.LL
THE
POINCARE-BENDIXSON
THEOREM
46
EXERCISES
51
1.2
POINCARE
MAPS:
THEORY,
CONSTRUCTION,
AND
EXAMPLES
64
1.2
A
POINCARE
MAPS:
EXAMPLES
64
1.2
B
VARYING
THE
CROSS-SECTION:
CONJUGACIES
OF
MAPS
89
1.2C
STRUCTURAL
STABILITY,
GENERICITY,
AND
TRANSVERSALITY
94
1.2
D
CONSTRUCTION
OF
THE
POINCARE
MAP
103
1.2
E
APPLICATION
TO
THE
DYNAMICS
OF
THE
DAMPED,
FORCED
DUFFING
OSCILLATOR
153
EXERCISES
175
XII
CONTENTS
2
METHODS
FOR
SIMPLIFYING
DYNAMICAL
SYSTEMS
193
2.1
CENTER
MANIFOLDS
193
2.1
A
CENTER
MANIFOLDS
FOR
VECTOR
FIELDS
194
2.1
B
CENTER
MANIFOLDS
DEPENDING
ON
PARAMETERS
198
2.1C
THE
INCLUSION
OF
LINEARLY
UNSTABLE
DIRECTIONS
203
2.
I
D
CENTER
MANIFOLDS
FOR
MAPS
204
2.1E
PROPERTIES
OF
CENTER
MANIFOLDS
210
2.2
NORMAL
FORMS
211
2.2
A
NORMAL
FORMS
FOR
VECTOR
FIELDS
212
2.2
B
NORMAL
FORMS
FOR
VECTOR
FIELDS
WITH
PARAMETERS
220
2.2C
NORMAL
FORMS
FOR
MAPS
225
2.2D
CONJUGACIES
AND
EQUIVALENCES
OF
VECTOR
FIELDS
229
2.3
FINAL
REMARKS
237
EXERCISES
239
3
LOCAL
BIFURCATIONS
253
3.1
BIFURCATION
OF
FIXED
POINTS
OF
VECTOR
FIELDS
253
3.1A
A
ZERO
EIGENVALUE
254
3.1B
A
PURE
IMAGINARY
PAIR
OF
EIGENVALUES:
THE
POINCARE-ANDRONOV-HOPF
BIFURCATION
270
3.1C
STABILITY
OF
BIFURCATIONS
UNDER
PERTURBATIONS
278
3.1D
THE
IDEA
OF
THE
CODIMENSION
OF
A
BIFURCATION
284
APPENDIX
1:
VERSAL
DEFORMATIONS
OF
FAMILIES
OF
MATRICES
305
3.1E
THE
DOUBLE-ZERO
EIGENVALUE
321
3.
1F
A
ZERO
AND
A
PURE
IMAGINARY
PAIR
OF
EIGENVALUES
331
3.2
BIFURCATIONS
OF
FIXED
POINTS
OF
MAPS
357
3.2
A
AN
EIGENVALUE
OF
1
358
3.2
B
AN
EIGENVALUE
OF
-
1
371
3.2C
A
PAIR
OF
EIGENVALUES
OF
MODULUS
1:
THE
NAIMARK-SACKER
BIFURCATION
374
3.2
D
THE
CODIMENSION
OF
LOCAL
BIFURCATIONS
OF
MAPS
381
3.3
ON
THE
INTERPRETATION
AND
APPLICATION
OF BIFURCATION
DIAGRAMS:
A
WORD
OF
CAUTION
384
EXERCISES
386
CONTENTS
XIII
4
SOME
ASPECTS
OF
GLOBAL
BIFURCATION
AND
CHAOS
420
4.1
THE
SMALE
HORSESHOE
420
4.1
A
DEFINITION
OF
THE
SMALE
HORSESHOE
MAP
421
4.1
B
CONSTRUCTION
OF
THE
INVARIANT
SET
423
4.1C
SYMBOLIC
DYNAMICS
430
4.
I
D
THE
DYNAMICS
ON
THE
INVARIANT
SET
433
4.
I
E
CHAOS
436
4.2
SYMBOLIC
DYNAMICS
438
4.2
A
THE
STRUCTURE
OF
THE
SPACE
OF
SYMBOL
SEQUENCES
439
4.2
B
THE
SHIFT
MAP
442
4.3
THE
CONLEY-MOSER
CONDITIONS,
OR
"
HOW
TO
PROVE
THAT
A
DYNAMICAL
SYSTEM
IS
CHAOTIC
"
443
4.3
A
THE
MAIN
THEOREM
444
4.3
B
SECTOR
BUNDLES
458
4.3C
HYPERBOLIC
INVARIANT
SETS
463
4.4
DYNAMICS
NEAR
HOMOCLINIC
POINTS
OF
TWO-
DIMENSIONAL
MAPS
470
4.5
MELNIKOV
'
S
METHOD
FOR
HOMOCLINIC
ORBITS
IN
TWO-
DIMENSIONAL,
TIME-PERIODIC
VECTOR
FIELDS
483
4.5
A
THE
GENERAL
THEORY
484
4.5
B
POINCARE
MAPS
AND
THE
GEOMETRY
OF
THE
MELNIKOV
FUNCTION
505
4.5C
SOME
PROPERTIES
OF
THE
MELNIKOV
FUNCTION
507
4.5D
RELATIONSHIP
WITH
THE
SUBHARMONIC
MELNIKOV
FUNCTION
509
4.5
E
HOMOCLINIC
AND
SUBHARMONIC
BIFURCATIONS
511
4.5
F
APPLICATION
TO
THE
DAMPED,
FORCED
DUFFING
OSCILLATOR
513
4.6
GEOMETRY
AND
DYNAMICS
IN
THE
TANGLE
519
4.6
A
PIPS
AND
LOBES
521
4.6
B
TRANSPORT
IN
PHASE
SPACE
526
4.6C
TECHNICAL
DETAILS
535
4.6
D
APPLICATION
TO
THE
MELNIKOV
THEORY
TO
TRANSPORT
538
XIV
CONTENTS
4.7
HOMOCLINIC
BIFURCATIONS:
CASCADES
OF
PERIOD-DOUBLING
AND
SADDLE-NODE
BIFURCATIONS
540
4.8
ORBITS
HOMOCLINIC
TO
HYPERBOLIC
FIXED
POINTS
IN
THREE-DIMENSIONAL
AUTONOMOUS
VECTOR
FIELDS
552
4.8
A
ORBITS
HOMOCLINIC
TO
A
SADDLE-POINT
WITH
PURELY
REAL
EIGENVALUES
556
4.8
B
ORBITS
HOMOCLINIC
TO
A
SADDLE-FOCUS
573
4.9
GLOBAL
BIFURCATIONS
ARISING
FROM
LOCAL
CODIMENSION-TWO
BIFURCATIONS
591
4.9A
THE
DOUBLE-ZERO
EIGENVALUE
592
4.9B
A
ZERO
AND
A
PURE
IMAGINARY
PAIR
OF
EIGENVALUES
595
4.10
LIAPUNOV
EXPONENTS
603
4.11
CHAOS
AND
STRANGE
ATTRACTORS
608
EXERCISES
616
BIBLIOGRAPHY
651
INDEX
667 |
| any_adam_object | 1 |
| author | Wiggins, Stephen ca. 20./21. Jh |
| author_GND | (DE-588)1247764664 |
| author_facet | Wiggins, Stephen ca. 20./21. Jh |
| author_role | aut |
| author_sort | Wiggins, Stephen ca. 20./21. Jh |
| author_variant | s w sw |
| building | Verbundindex |
| bvnumber | BV011300498 |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.8 |
| callnumber-search | QA614.8 |
| callnumber-sort | QA 3614.8 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 520 SK 540 SK 810 UG 3900 |
| classification_tum | MAT 344f MAT 587f |
| ctrlnum | (OCoLC)35042439 (DE-599)BVBBV011300498 |
| discipline | Physik Mathematik |
| edition | 4. print. |
| format | Book |
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| genre | 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV011300498 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T03:39:55Z |
| institution | BVB |
| isbn | 3540970037 0387970037 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007590802 |
| oclc_num | 35042439 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM |
| owner_facet | DE-91 DE-BY-TUM |
| physical | XIV, 672 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Wiggins, Stephen ca. 20./21. Jh. Verfasser (DE-588)1247764664 aut Introduction to applied nonlinear dynamical systems and chaos Stephen Wiggins 4. print. New York [u.a.] Springer 1996 XIV, 672 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 2 Literaturverz. S. 651 - 666 Chaotic behavior in systems Differentiable dynamical systems Nonlinear theories Nichtlineare Theorie (DE-588)4251279-7 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Chaos (DE-588)4191419-3 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Chaotisches System (DE-588)4316104-2 s Nichtlineares dynamisches System (DE-588)4126142-2 s DE-604 Chaostheorie (DE-588)4009754-7 s 2\p DE-604 Chaos (DE-588)4191419-3 s 3\p DE-604 Nichtlineare Theorie (DE-588)4251279-7 s 4\p DE-604 Differenzierbares dynamisches System (DE-588)4137931-7 s 5\p DE-604 Texts in applied mathematics 2 (DE-604)BV002476038 2 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007590802&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wiggins, Stephen ca. 20./21. Jh Introduction to applied nonlinear dynamical systems and chaos Texts in applied mathematics Chaotic behavior in systems Differentiable dynamical systems Nonlinear theories Nichtlineare Theorie (DE-588)4251279-7 gnd Chaostheorie (DE-588)4009754-7 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Chaos (DE-588)4191419-3 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4251279-7 (DE-588)4009754-7 (DE-588)4126142-2 (DE-588)4137931-7 (DE-588)4191419-3 (DE-588)4316104-2 (DE-588)4143389-0 |
| title | Introduction to applied nonlinear dynamical systems and chaos |
| title_auth | Introduction to applied nonlinear dynamical systems and chaos |
| title_exact_search | Introduction to applied nonlinear dynamical systems and chaos |
| title_full | Introduction to applied nonlinear dynamical systems and chaos Stephen Wiggins |
| title_fullStr | Introduction to applied nonlinear dynamical systems and chaos Stephen Wiggins |
| title_full_unstemmed | Introduction to applied nonlinear dynamical systems and chaos Stephen Wiggins |
| title_short | Introduction to applied nonlinear dynamical systems and chaos |
| title_sort | introduction to applied nonlinear dynamical systems and chaos |
| topic | Chaotic behavior in systems Differentiable dynamical systems Nonlinear theories Nichtlineare Theorie (DE-588)4251279-7 gnd Chaostheorie (DE-588)4009754-7 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Chaos (DE-588)4191419-3 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Chaotic behavior in systems Differentiable dynamical systems Nonlinear theories Nichtlineare Theorie Chaostheorie Nichtlineares dynamisches System Differenzierbares dynamisches System Chaos Chaotisches System Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007590802&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT wigginsstephen introductiontoappliednonlineardynamicalsystemsandchaos |