Hamiltonian systems and their integrability:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
Providence, RI
American Math. Soc. <<[u.a.]>>
2008
|
| Schriftenreihe: | SMF/AMS texts and monographs
15 Cours spécialisés 8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XII, 149 S. |
| ISBN: | 9780821844137 |
Internformat
MARC
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| 240 | 1 | 0 | |a Systèmes hamiltoniens et leur intégrabilité |
| 245 | 1 | 0 | |a Hamiltonian systems and their integrability |c Michele Audin |
| 264 | 1 | |a Providence, RI |b American Math. Soc. <<[u.a.]>> |c 2008 | |
| 300 | |a XII, 149 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 490 | 1 | |a Cours spécialisés |v 8 | |
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Datensatz im Suchindex
| _version_ | 1804140645731794944 |
|---|---|
| adam_text | Contents
Introduction
Chapter I. Introduction to
Integrable
Systems
1
1.1. Symplectic Manifolds
1
1.2.
Hamiltonian Systems, Examples
6
1.3.
Completely
Integrable
Systems
10
1.4.
Geodesic Flows
13
1.5.
Appendix: The Theorem of Darboux
18
Exercises
19
Chapter II. Action-Angle Variables
25
II.
1.
Hamiltonian Torus Actions
25
11.2. The Amold-Liouville Theorem
29
11.3. Examples
36
Exercises
40
Chapter III. Integrability and Galois Groups
45
The Arnold-Liouville Theorem, Revisited Through Differential Galois
Theory
45
ULI.
Variational Equations, Galois Groups, and First Integrals
46
111.2. The Case of a Hamiltonian System
52
111.3. The Case of an
Integrable
System
55
111.4. Towards Applications: The Reduction
64
111.5. The Example of the
Hénon-Heiles
System
69
111.6. Appendix: Proof of Ziglin s Lemma
72
Exercises
76
Chapter IV. An Introduction to Lax Equations
81
The Arnold-Liouville Theorem, Revisited Through Lax Equations
81
ГУМ.
Why Algebraic Curves?
82
IV.2. A Linearization Theorem
85
IV.3. The case of Geodesies on Quadrics
90
IV.4. Appendix: How to Construct Lax Equations (an Overview)
103
Exercises
109
vii
viii CONTENTS
Appendices
Appendix A. What One Needs to Know About Differential Galois Theory
117
A.I. Differential Fields
117
A.
2.
The Picard-Vessiot Extension
118
A.3. The Galois Group
120
A.4. The Galois Group of a Hamiltonian System is Symplectic
122
A.5. An Example: the Airy Equation
124
Easy Exercises on Differential Galois Theory
128
Appendix B. What One Needs to Know About Algebraic Curves
131
B.I. Complex Curves and Riemann Surfaces
131
B.2. Line Bundles on Curves
133
B.3. Sheaves and Cocycles
135
B.4. The
Picard
Group, the Riemann-Roch Theorem, the Jacobian
136
Exercises to Check Comprehension of the Definitions
139
Bibliography
141
Index
145
|
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| id | DE-604.BV024624116 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:03:16Z |
| institution | BVB |
| isbn | 9780821844137 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018595954 |
| oclc_num | 229750200 |
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| owner_facet | DE-83 DE-384 DE-355 DE-BY-UBR |
| physical | XII, 149 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Math. Soc. <<[u.a.]>> |
| record_format | marc |
| series | SMF/AMS texts and monographs Cours spécialisés |
| series2 | SMF/AMS texts and monographs Cours spécialisés |
| spelling | Audin, Michèle 1954- Verfasser (DE-588)14151552X aut Systèmes hamiltoniens et leur intégrabilité Hamiltonian systems and their integrability Michele Audin Providence, RI American Math. Soc. <<[u.a.]>> 2008 XII, 149 S. txt rdacontent n rdamedia nc rdacarrier SMF/AMS texts and monographs 15 Cours spécialisés 8 Includes bibliographical references and index Hamiltonian systems Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s DE-604 SMF/AMS texts and monographs 15 (DE-604)BV013184477 15 Cours spécialisés 8 (DE-604)BV012699276 8 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018595954&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Audin, Michèle 1954- Hamiltonian systems and their integrability SMF/AMS texts and monographs Cours spécialisés Hamiltonian systems Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4139943-2 |
| title | Hamiltonian systems and their integrability |
| title_alt | Systèmes hamiltoniens et leur intégrabilité |
| title_auth | Hamiltonian systems and their integrability |
| title_exact_search | Hamiltonian systems and their integrability |
| title_full | Hamiltonian systems and their integrability Michele Audin |
| title_fullStr | Hamiltonian systems and their integrability Michele Audin |
| title_full_unstemmed | Hamiltonian systems and their integrability Michele Audin |
| title_short | Hamiltonian systems and their integrability |
| title_sort | hamiltonian systems and their integrability |
| topic | Hamiltonian systems Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Hamiltonian systems Hamiltonsches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018595954&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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