Quasi-periodic motions in families of dynamical systems: order amidst chaos
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1996
|
| Series: | Lecture notes in mathematics
1645 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 195 S. graph. Darst. |
| ISBN: | 3540620257 |
Staff View
MARC
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| 245 | 1 | 0 | |a Quasi-periodic motions in families of dynamical systems |b order amidst chaos |c Hendrik W. Broer ; George B. Huitema ; Mikhail B. Sevryuk |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1996 | |
| 300 | |a XI, 195 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Tore (Géométrie) | |
| 650 | 4 | |a Flows (Differentiable dynamical systems) | |
| 650 | 4 | |a Hamiltonian systems | |
| 650 | 4 | |a Perturbation (Mathematics) | |
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Record in the Search Index
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| adam_text |
HENDRIK W. BROER GEORGE B
. HUITEMA
MIKHAIL B
. SEVRYUK
QUASI-PERIODIC MOTIONS
IN FAMILIES
OF DYNAMICAL SYSTEMS
ORDER AMIDST CHAOS
JF
L SPRINGE
R
CONTENT
S
1 INTRODUCTIO
N AN
D EXAMPLE
S 1
1.1 A PRELIMINAR
Y SETTIN
G OF TH
E PROBLE
M 1
1.1.1 DEFINITIONS 2
1.1.2 CONTEXT
S 5
1.2 OCCURRENC
E OF QUASI-PERIODICIT
Y 6
1.2.1 QUASI-PERIODI
C ATTRACTOR
S 6
1.2.2 QUASI-PERIODI
C MOTION
S IN CONSERVATIVE EXAMPLE
S 13
1.2.3 QUASI-PERIODI
C RESPONSE
S 15
1.3 A FURTHE
R SETTIN
G OF TH
E PROBLE
M 16
1.3.1 TH
E MAI
N PROBLE
M 16
1.3.2 CONTEXT
S REVISITED
: DEFINITIONS 18
1.3.3 INTEGRABILIT
Y 21
1.4 SUMMAR
Y 29
1.4.1 A HEURISTI
C PRINCIPL
E 29
1.4.2 TH
E HAMILTONIA
N COISOTROPIC CONTEX
T 31
1.5 SMALL DIVISORS AN
D WHITNEY-SMOOTHNES
S IN 1-BITE PROBLEM
S 32
1.5.1 EXAMPLE
S AN
D FORMAL SOLUTIONS 32
1.5.2 CONVERGENCE AN
D WHITNEY-SMOOTHNES
S 35
2 TH
E CONJUGAC
Y THEOR
Y 4
1
2.1 PRELIMINAR
Y CONSIDERATION
S 41
2.2 WHITNEY-SMOOT
H FAMILIES OF TORI
: A DEFINITION 44
2.3 QUASI-PERIODI
C STABILIT
Y 47
2.3.1 TH
E DISSIPATIV
E CONTEX
T 48
2.3.2 TH
E VOLUME PRESERVIN
G CONTEX
T (P 2) 49
2.3.3 TH
E VOLUME PRESERVIN
G CONTEX
T (P = 1) 51
2.3.4 TH
E HAMILTONIA
N ISOTROPI
C CONTEX
T 52
2.3.5 TH
E REVERSIBLE CONTEX
T 1 53
2.4 TH
E PRELIMINAR
Y PARAMETE
R REDUCTIO
N 55
2.4.1 TH
E DISSIPATIV
E CONTEX
T 55
2.4.2 TH
E VOLUME PRESERVIN
G CONTEX
T (P 2) 56
2.4.3 TH
E VOLUME PRESERVIN
G CONTEX
T (P = 1) 56
2.4.4 TH
E HAMILTONIA
N ISOTROPI
C CONTEX
T 57
2.4.5 TH
E REVERSIBLE CONTEX
T 1 58
2.4.6 TH
E PROOF IN TH
E HAMILTONIA
N ISOTROPIC CONTEX
T 58
2.5 TH
E FINAL PARAMETE
R REDUCTIO
N 60
X CONTENTS
2.5.1 DIOPHANTIN
E APPROXIMATION
S ON SUBMANIFOLDS 61
2.5.2 TH
E DISSIPATIV
E CONTEX
T YY-. 63
2.5.3 TH
E VOLUME PRESERVIN
G CONTEX
T (P 2) 65
2.5.4 TH
E VOLUME PRESERVIN
G CONTEX
T (P = 1) 65
2.5.5 TH
E HAMILTONIA
N ISOTROPI
C CONTEXT 66
2.5.6 TH
E REVERSIBLE CONTEX
T 1 67
2.5.7 TH
E PROOF IN TH
E REVERSIBLE CONTEX
T 1 68
2.6 CONVERSE KAM THEOR
Y 70
2.7 WHITNEY-SMOOT
H FAMILIES OF TORI
: RESULT
S 73
3 TH
E CONTINUATIO
N THEOR
Y 7
7
3.1 ANALYTIC CONTINUATIO
N OF TOR
I 77
3.2 WHITNEY-SMOOT
H FAMILIES OF TORI
: FURTHER RESULT
S 82
4 COMPLICATE
D WHITNEY-SMOOT
H FAMILIE
S 8
3
4.1 EXCITATIO
N OF NORMA
L MODE
S 83
4.1.1 TH
E CONCEPT 83
4.1.2 TH
E REVERSIBLE CONTEX
T (M + S 1) 85
4.1.3 TH
E REVERSIBLE CONTEX
T (M = S = 0 AN
D N 1) 88
4.1.4 TH
E HAMILTONIA
N CONTEX
T (N + S 1) 96
4.1.5 TH
E MEASURE ESTIMATE
S 101
4.2 RESONANCE ZONES 102
4.2.1 POINCARE TRAJECTORIE
S 104
4.2.2 TRESHCHEV TOR
I 106
4.2.3 STABILIT
Y OF TH
E ACTIO
N VARIABLE
S 109
4.2.4 STICKINESS OF TH
E INVARIAN
T TOR
I 112
4.2.5 PECULIARITIE
S OF TH
E REVERSIBLE CONTEX
T 114
4.3 QUASI-PERIODIC BIFURCATION THEOR
Y ; 115
5 CONCLUSION
S 12
3
5.1 ANALOGUES AN
D NON-ANALOGUE
S FOR DIFFEOMORPHISMS 123
5.1.1 DEFINITIONS 123
5.1.2 CONTEXT
S 124
5.1.3 PECULIARITIE
S OF TH
E SYMPLECTIC AN
D REVERSIBLE CONTEXT
S 125
5.1.4 RESULT
S 126
5.1.5 PROOFS 128
5.1.6 PERIODICALLY INVARIANT TOR
I 130
5.1.7 TH
E POINCAR
E SECTION REDUCTIO
N 130
5.2 DENSITY POINT
S OF QUASI-PERIODICIT
Y 131
5.3 INVARIAN
T TOR
I AN
D STABILIT
Y OF MOTIO
N 135
5.3.1 AN ELLIPTIC EQUILIBRIU
M OF A TWO-DEGREE-OF-FREEDOM HAMILTONIA
N VEC
TO
R FIELD 135
5.3.2 AN ELLIPTIC EQUILIBRIU
M OF A REVERSIBLE VECTOR FIELD IN R
4
137
CONTENTS XI
6 APPENDICE
S 14
1
6.
I PROO
F OF TH
E DISSIPATIV
E MAI
N THEORE
M 141
6.1.1 FORMULATIO
N OF TH
E STABILIT
Y THEORE
M 141
6.1.2 PRELIMINAR
Y REMARK
S 143
6.1.3 PROO
F 145
6.1.4 WHITNEY-SMOOTHNESS
: SOME THEOR
Y 155
6.2 CONJECTURA
L NEW CONTEXT
S 157
6.3 TH
E BRUN
O THEOR
Y 161
6.4 A PROOF OF TH
E DIOPHANTIN
E APPROXIMATIO
N IEMM
A 165
BIBLIOGRAPH
Y 16
9
INDE
X 19
3 |
| any_adam_object | 1 |
| author | Broer, Hendrik W. 1950- Huitema, George B. Sevrjuk, Michail B. |
| author_GND | (DE-588)124653782 |
| author_facet | Broer, Hendrik W. 1950- Huitema, George B. Sevrjuk, Michail B. |
| author_role | aut aut aut |
| author_sort | Broer, Hendrik W. 1950- |
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| dewey-ones | 514 - Topology 510 - Mathematics |
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| dewey-search | 514/.74 510 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011068198 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:38:20Z |
| institution | BVB |
| isbn | 3540620257 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007413644 |
| oclc_num | 246273500 |
| open_access_boolean | |
| owner | DE-20 DE-91G DE-BY-TUM DE-29T DE-824 DE-12 DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-20 DE-91G DE-BY-TUM DE-29T DE-824 DE-12 DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XI, 195 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Broer, Hendrik W. 1950- Verfasser (DE-588)124653782 aut Quasi-periodic motions in families of dynamical systems order amidst chaos Hendrik W. Broer ; George B. Huitema ; Mikhail B. Sevryuk Berlin [u.a.] Springer 1996 XI, 195 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1645 Dynamische systemen gtt Flots (Dynamique différentiable) Perturbation (Mathématiques) Quasiperiodiciteit gtt Systèmes hamiltoniens Tore (Géométrie) Flows (Differentiable dynamical systems) Hamiltonian systems Perturbation (Mathematics) Torus (Geometry) Quasiperiodizität (DE-588)4247312-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Quasiperiodischer Torus (DE-588)4234594-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Quasiperiodizität (DE-588)4247312-3 s DE-604 Quasiperiodischer Torus (DE-588)4234594-7 s Huitema, George B. Verfasser aut Sevrjuk, Michail B. Verfasser aut Lecture notes in mathematics 1645 (DE-604)BV000676446 1645 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007413644&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Broer, Hendrik W. 1950- Huitema, George B. Sevrjuk, Michail B. Quasi-periodic motions in families of dynamical systems order amidst chaos Lecture notes in mathematics Dynamische systemen gtt Flots (Dynamique différentiable) Perturbation (Mathématiques) Quasiperiodiciteit gtt Systèmes hamiltoniens Tore (Géométrie) Flows (Differentiable dynamical systems) Hamiltonian systems Perturbation (Mathematics) Torus (Geometry) Quasiperiodizität (DE-588)4247312-3 gnd Dynamisches System (DE-588)4013396-5 gnd Quasiperiodischer Torus (DE-588)4234594-7 gnd |
| subject_GND | (DE-588)4247312-3 (DE-588)4013396-5 (DE-588)4234594-7 |
| title | Quasi-periodic motions in families of dynamical systems order amidst chaos |
| title_auth | Quasi-periodic motions in families of dynamical systems order amidst chaos |
| title_exact_search | Quasi-periodic motions in families of dynamical systems order amidst chaos |
| title_full | Quasi-periodic motions in families of dynamical systems order amidst chaos Hendrik W. Broer ; George B. Huitema ; Mikhail B. Sevryuk |
| title_fullStr | Quasi-periodic motions in families of dynamical systems order amidst chaos Hendrik W. Broer ; George B. Huitema ; Mikhail B. Sevryuk |
| title_full_unstemmed | Quasi-periodic motions in families of dynamical systems order amidst chaos Hendrik W. Broer ; George B. Huitema ; Mikhail B. Sevryuk |
| title_short | Quasi-periodic motions in families of dynamical systems |
| title_sort | quasi periodic motions in families of dynamical systems order amidst chaos |
| title_sub | order amidst chaos |
| topic | Dynamische systemen gtt Flots (Dynamique différentiable) Perturbation (Mathématiques) Quasiperiodiciteit gtt Systèmes hamiltoniens Tore (Géométrie) Flows (Differentiable dynamical systems) Hamiltonian systems Perturbation (Mathematics) Torus (Geometry) Quasiperiodizität (DE-588)4247312-3 gnd Dynamisches System (DE-588)4013396-5 gnd Quasiperiodischer Torus (DE-588)4234594-7 gnd |
| topic_facet | Dynamische systemen Flots (Dynamique différentiable) Perturbation (Mathématiques) Quasiperiodiciteit Systèmes hamiltoniens Tore (Géométrie) Flows (Differentiable dynamical systems) Hamiltonian systems Perturbation (Mathematics) Torus (Geometry) Quasiperiodizität Dynamisches System Quasiperiodischer Torus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007413644&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT broerhendrikw quasiperiodicmotionsinfamiliesofdynamicalsystemsorderamidstchaos AT huitemageorgeb quasiperiodicmotionsinfamiliesofdynamicalsystemsorderamidstchaos AT sevrjukmichailb quasiperiodicmotionsinfamiliesofdynamicalsystemsorderamidstchaos |