Symmetry and perturbation theory in nonlinear dynamics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1999
|
| Schriftenreihe: | [Lecture notes in physics / M]
57 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 208 S. |
| ISBN: | 3540659048 |
Internformat
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| 245 | 1 | 0 | |a Symmetry and perturbation theory in nonlinear dynamics |c Giampaolo Cicogna ; Giuseppe Gaeta |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XI, 208 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Formes normales (mathématiques) |2 ram | |
| 650 | 4 | |a Perturbation (Mathématiques) | |
| 650 | 7 | |a Perturbation (mathématiques) |2 ram | |
| 650 | 4 | |a Symétrie (Physique) | |
| 650 | 7 | |a Symétrie (physique) |2 ram | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Normal forms (Mathematics) | |
| 650 | 4 | |a Perturbation (Mathematics) | |
| 650 | 4 | |a Symmetry (Physics) | |
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Datensatz im Suchindex
| _version_ | 1804127453485989888 |
|---|---|
| adam_text | GIAMPAOLO CICOGNA GIUSEPPE GAETA
SYMMETR
Y
AN
D PERTURBATIO
N THEOR
Y
I
N NONLINEA
R DYNAMIC
S
H
P SPRINGER
CONTENT
S
INTRODUCTIO
N 1
1. PERTURBATIO
N THEOR
Y 3
2. OTHE
R TOOLS T
O STUD
Y NONLINEA
R SYSTEM
S AN
D SYMMETR
Y 6
3
. WH
Y NONLINEA
R SYMMETRIES
? 8
4. WH
Y NORMA
L FORMS
? 10
5. NORMA
L FORM
S AN
D HIGHER-LEVEL PERTURBATIO
N THEOR
Y 14
6. DIREC
T APPLICATION
S OF NORMA
L FORM
S THEOR
Y IN PHYSIC
S 16
I
. SYMMETR
Y AN
D DIFFERENTIA
L EQUATION
S 19
1. GEOMETRICA
L SETTIN
G 21
2. INVARIANC
E OF EQUATION
S AN
D OF SOLUTION
S 24
3. REDUCTIO
N AN
D SOLUTION OF ORDINAR
Y DIFFERENTIAL EQUATION
S 29
4. REDUCTIO
N AN
D SOLUTIO
N OF PARTIA
L DIFFERENTIAL EQUATION
S 33
5. O
N TH
E APPLICATIO
N OF SYMMETR
Y METHOD
S 38
APPENDIX
. TH
E PROLONGATIO
N FORMUL
A 39
II
. DYNAMICA
L SYSTEM
S 41
1. DYNAMICA
L SYSTEM
S AN
D FLOWS 41
2. SINGULA
R POINT
S AN
D INVARIAN
T MANIFOLDS 43
3. CONSERVED QUANTITIE
S 47
4. PERTURBATIV
E EXPANSIO
N 48
5. POINCARE-DULA
C NORMA
L FORM
S 51
6. BIRKHOFF-GUSTAVSO
N NORMA
L FORM
S 56
7. BIFURCATIO
N THEOR
Y 61
APPENDIX
. LIE TRANSFORM
S 64
X CONTENTS
III
. SYMMETRIE
S O
F DYNAMICA
L SYSTEM
S 67
1. SYMMETRIES OF DYNAMICA
L SYSTEM
S 68
2. LIE-POINT TIME-INDEPENDEN
T SYMMETRIE
S 69
3. CONSTANT
S OF MOTION AN
D TH
E MODUL
E STRUCTUR
E
OF TH
E SYMMETR
Y ALGEBR
A 71
4. SYMMETR
Y AN
D TOPOLOGY OF TRAJECTORIE
S 72
5. TIME-DEPENDEN
T SYMMETRIE
S 75
6. ORBITA
L SYMMETRIE
S 77
7. APPROXIMAT
E SYMMETRIE
S 78
APPENDIX
. O
N TH
E MODUL
E STRUCTUR
E 81
IV
. NORMA
L FORM
S AN
D SYMMETRIE
S FOR DYNAMICA
L SYSTEM
S 83
1. PERTURBATIV
E EXPANSIO
N OF DETERMININ
G EQUATION
S 83
2. RECURSIV
E DETERMINATIO
N OF SYMMETRIE
S 85
3. APPROXIMAT
E SYMMETRIE
S 88
4. SYMMETR
Y CHARACTERIZATIO
N OF POINCARE-DULA
C NORMA
L FORMS 89
5. NONLINEA
R SYMMETRIE
S AN
D NORMA
L FORM
S 91
6. LINEA
R SYMMETRIE
S AN
D NORMA
L FORMS 96
7. O
N LINEA
R AN
D NONLINEA
R SYMMETRIE
S 97
8. SYMMETR
Y FOR SYSTEM
S IN NORMA
L FORM 99
9. REDUCTIO
N T
O NORMA
L FOR
M OF A NILPOTEN
T LIE ALGEBR
A 101
10. NON-SEMISIMPL
E NORMA
L FORM
S 104
11
. TH
E LINEARIZATIO
N OF A DYNAMICA
L SYSTE
M 108
12. PARTIA
L JOIN
T NORMA
L FOR
M FOR NON-NILPOTEN
T ALGEBRAS 109
APPENDIX
. SOME RESULT
S ON MATRICE
S AN
D LIE ALGEBRA
S 112
V
. NORMA
L FORM
S AN
D SYMMETRIE
S FOR HAMILTONIA
N SYSTEM
S 115
1. BIRKHOFF-GUSTAVSON NORMA
L FORM
S 115
2. BIRKHOFF-GUSTAVSON NORMA
L FORM
S WIT
H SYMMETRIE
S 118
3. TH
E CAS
E OF D-DIMENSIONA
L ALGEBRAS OF SYMMETRIE
S 124
4. PERTURBATIV
E CONSTRUCTIO
N OF SYMMETRIE
S 126
5. TH
E NON-NORMA
L CAS
E 128
6. TH
E NORMALIT
Y OF TH
E HOMOLOGICAL OPERATO
R 132
CONTENTS XI
VI
. CONVERGENC
E O
F TH
E NORMALIZIN
G TRANSFORMATION
S 135
1. CONDITION
S ENSURIN
G CONVERGENCE 135
2. NORMALIZIN
G TRANSFORMATION
S IN TH
E PRESENC
E OF SYMMETRIE
S 139
3. CONVERGENCE AN
D SYMMETRIES
: A GENERA
L RESUL
T 141
4. CONVERGENC
E AN
D SYMMETRIES
: A SPECIAL CAS
E 144
5. CONVERGENCE IN TH
E CAS
E OF HAMILTONIA
N PROBLEM
S 148
VII
. INVARIAN
T MANIFOLD
S 151
1. SOME PRELIMINAR
Y RESULT
S ON FLOW INVARIAN
T MANIFOLDS 151
2. REDUCTIO
N T
O A CENTE
R MANIFOLD 154
3
. NORMA
L FORM
S 155
4. SHOSHITAISHVIL
I THEORE
M AN
D CENTE
R MANIFOLDS 156
5. SOME EXAMPLE
S 158
VIII
. FURTHE
R NORMALIZATIO
N 163
1. HIGHER-ORDE
R TERM
S IN POINCAR
E TRANSFORMATION
S 164
2. TH
E HOMOLOGICAL OPERATOR
S 166
3. NON-UNIQUENES
S OF POINCAR
E NORMA
L FORM
S 166
4. POINCAR
E RENORMALIZATIO
N 167
5. RENORMALIZATIO
N BY ITERATE
D NORMALIZATION
S 171
6. EXAMPLES
: PLANA
R VECTOR FIELD
S 173
7. TH
E HAMILTONIA
N CAS
E 177
8. RENORMALIZE
D FORM
S IN TH
E PRESENC
E OF SYMMETR
Y 179
IX
. ASYMPTOTI
C SYMMETRIE
S 183
1. NOTATIO
N AN
D BASIC SETS 184
2. INDUCE
D ACTION
S ON FUNCTION
S AN
D EQUATION
S 185
3. SYMMETRIE
S AN
D ASYMPTOTI
C SYMMETRIE
S 187
4. ASYMPTOTI
C SYMMETRIE
S AN
D SPACE-TIM
E ASYMPTOTI
C PROPERTIE
S 189
REFERENCE
S
193
|
| any_adam_object | 1 |
| author | Cicogna, Giampaolo 1942- Gaeta, Giuseppe 1959- |
| author_GND | (DE-588)12140420X (DE-588)121404188 |
| author_facet | Cicogna, Giampaolo 1942- Gaeta, Giuseppe 1959- |
| author_role | aut aut |
| author_sort | Cicogna, Giampaolo 1942- |
| author_variant | g c gc g g gg |
| building | Verbundindex |
| bvnumber | BV012782422 |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.8 |
| callnumber-search | QA614.8 |
| callnumber-sort | QA 3614.8 |
| callnumber-subject | QA - Mathematics |
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| classification_tum | PHY 066f |
| ctrlnum | (OCoLC)42476780 (DE-599)BVBBV012782422 |
| dewey-full | 515/.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV012782422 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:33:35Z |
| institution | BVB |
| isbn | 3540659048 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008693693 |
| oclc_num | 42476780 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-634 DE-11 DE-188 |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-634 DE-11 DE-188 |
| physical | XI, 208 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series2 | [Lecture notes in physics / M] |
| spelling | Cicogna, Giampaolo 1942- Verfasser (DE-588)12140420X aut Symmetry and perturbation theory in nonlinear dynamics Giampaolo Cicogna ; Giuseppe Gaeta Berlin [u.a.] Springer 1999 XI, 208 S. txt rdacontent n rdamedia nc rdacarrier [Lecture notes in physics / M] 57 Dynamique différentiable Dynamique différentiable ram Formes normales (Mathématiques) Formes normales (mathématiques) ram Perturbation (Mathématiques) Perturbation (mathématiques) ram Symétrie (Physique) Symétrie (physique) ram Differentiable dynamical systems Normal forms (Mathematics) Perturbation (Mathematics) Symmetry (Physics) Störungstheorie (DE-588)4128420-3 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Normalform (DE-588)4172025-8 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s Störungstheorie (DE-588)4128420-3 s Symmetrie (DE-588)4058724-1 s DE-604 Nichtlineares dynamisches System (DE-588)4126142-2 s Normalform (DE-588)4172025-8 s Gaeta, Giuseppe 1959- Verfasser (DE-588)121404188 aut M] [Lecture notes in physics 57 (DE-604)BV021852221 57 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008693693&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cicogna, Giampaolo 1942- Gaeta, Giuseppe 1959- Symmetry and perturbation theory in nonlinear dynamics Dynamique différentiable Dynamique différentiable ram Formes normales (Mathématiques) Formes normales (mathématiques) ram Perturbation (Mathématiques) Perturbation (mathématiques) ram Symétrie (Physique) Symétrie (physique) ram Differentiable dynamical systems Normal forms (Mathematics) Perturbation (Mathematics) Symmetry (Physics) Störungstheorie (DE-588)4128420-3 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd Symmetrie (DE-588)4058724-1 gnd Normalform (DE-588)4172025-8 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4126142-2 (DE-588)4126141-0 (DE-588)4058724-1 (DE-588)4172025-8 |
| title | Symmetry and perturbation theory in nonlinear dynamics |
| title_auth | Symmetry and perturbation theory in nonlinear dynamics |
| title_exact_search | Symmetry and perturbation theory in nonlinear dynamics |
| title_full | Symmetry and perturbation theory in nonlinear dynamics Giampaolo Cicogna ; Giuseppe Gaeta |
| title_fullStr | Symmetry and perturbation theory in nonlinear dynamics Giampaolo Cicogna ; Giuseppe Gaeta |
| title_full_unstemmed | Symmetry and perturbation theory in nonlinear dynamics Giampaolo Cicogna ; Giuseppe Gaeta |
| title_short | Symmetry and perturbation theory in nonlinear dynamics |
| title_sort | symmetry and perturbation theory in nonlinear dynamics |
| topic | Dynamique différentiable Dynamique différentiable ram Formes normales (Mathématiques) Formes normales (mathématiques) ram Perturbation (Mathématiques) Perturbation (mathématiques) ram Symétrie (Physique) Symétrie (physique) ram Differentiable dynamical systems Normal forms (Mathematics) Perturbation (Mathematics) Symmetry (Physics) Störungstheorie (DE-588)4128420-3 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd Symmetrie (DE-588)4058724-1 gnd Normalform (DE-588)4172025-8 gnd |
| topic_facet | Dynamique différentiable Formes normales (Mathématiques) Formes normales (mathématiques) Perturbation (Mathématiques) Perturbation (mathématiques) Symétrie (Physique) Symétrie (physique) Differentiable dynamical systems Normal forms (Mathematics) Perturbation (Mathematics) Symmetry (Physics) Störungstheorie Nichtlineares dynamisches System Nichtlineare Dynamik Symmetrie Normalform |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008693693&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021852221 |
| work_keys_str_mv | AT cicognagiampaolo symmetryandperturbationtheoryinnonlineardynamics AT gaetagiuseppe symmetryandperturbationtheoryinnonlineardynamics |