Differential Galois theory and non-integrability of Hamiltonian systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Basel [u.a.]
Birkhäuser
1999
|
| Series: | Progress in mathematics
179 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 159 - 165 |
| Physical Description: | XIV, 165 S. graph. Darst. |
| ISBN: | 376436078X 081766078X |
Staff View
MARC
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| 100 | 1 | |a Morales Ruiz, Juan J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differential Galois theory and non-integrability of Hamiltonian systems |c Juan J. Morales Ruiz |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1999 | |
| 300 | |a XIV, 165 S. |b graph. Darst. | ||
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| 490 | 1 | |a Progress in mathematics |v 179 | |
| 500 | |a Literaturverz. S. 159 - 165 | ||
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| 650 | 7 | |a Hamilton-vergelijkingen |2 gtt | |
| 650 | 4 | |a Systèmes hamiltoniens | |
| 650 | 7 | |a Systèmes hamiltoniens |2 ram | |
| 650 | 4 | |a Differential algebra | |
| 650 | 4 | |a Galois theory | |
| 650 | 4 | |a Hamiltonian systems | |
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Record in the Search Index
| _version_ | 1804127311188983808 |
|---|---|
| adam_text | Contents
1 Introduction 1
2 Differential Galois Theory
2.1 Algebraic groups 7
2.2 Classical approach 11
2.3 Meromorphic connections 15
2.4 The Tannakian approach 24
2.5 Stokes multipliers 25
2.6 Coverings and differential Galois groups 28
2.7 Kovacic s algorithm 29
2.8 Examples 33
2.8.1 The hypergeometric equation 33
2.8.2 The Bessel equation 34
2.8.3 The confluent hypergeometric equation 36
2.8.4 The Lame equation 37
3 Hamiltoniaii Systems
3.1 Definitions 44
3.2 Complete integrability 48
3.3 Three non-integrability theorems 52
3.4 Some properties of Poisson algebras 57
4 Non-integrability Theorems
4.1 Variational equations 66
4.1.1 Singular curves 66
4.1.2 Meromorphic connection associated with
the variational equation 70
4.1.3 Reduction to normal variational equations 72
4.1.4 Reduction from the Tannakian point of view 78
4.2 Main results 80
4.3 Examples . . r 90
xiv Contents
5 Three Models
5.1 Homogeneous potentials 97
5.1.1 The model 97
5.1.2 Non-integrability theorem 98
5.1.3 Examples 101
5.2 The Bianchi IX cosmological model 105
5.2.1 The model 105
5.2.2 Non-integrability 107
5.3 Sitnikov s Three-Body Problem 109
5.3.1 The model 109
5.3.2 Non-integrability 110
6 An Application of the Lame Equation
6.1 Computation of the potentials 112
6.2 Non-integrability criterion 115
6.3 Examples 123
6.4 The homogeneous Henon-Heiles potential 126
7 A Connection with Chaotic Dynamics
7.1 Grotta-Ragazzo interpretation of
Lerman s theorem 132
7.2 Differential Galois approach 133
7.3 Example 135
8 Complementary Results and Conjectures
8.1 Two additional applications 139
8.2 A conjecture about the dynamic 142
8.3 Higher-order variational equations 142
8.3.1 A conjecture 142
8.3.2 An application 146
A Meromorphic Bundles 149
B Galois Groups and Finite Coverings 153
C Connections with Structure Group 157
Bibliography 159
Index 167
|
| any_adam_object | 1 |
| author | Morales Ruiz, Juan J. |
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| id | DE-604.BV012653502 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:31:20Z |
| institution | BVB |
| isbn | 376436078X 081766078X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008597374 |
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| physical | XIV, 165 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Morales Ruiz, Juan J. Verfasser aut Differential Galois theory and non-integrability of Hamiltonian systems Juan J. Morales Ruiz Basel [u.a.] Birkhäuser 1999 XIV, 165 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 179 Literaturverz. S. 159 - 165 Algèbre différentielle Algèbre différentielle ram Differentiaalvergelijkingen gtt Galois, Théorie de Galois, Théorie de ram Galois-theorie gtt Hamilton-vergelijkingen gtt Systèmes hamiltoniens Systèmes hamiltoniens ram Differential algebra Galois theory Hamiltonian systems Nichtintegrables System (DE-588)4462790-7 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Differentialalgebra (DE-588)4134657-9 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Differentialalgebra (DE-588)4134657-9 s Galois-Theorie (DE-588)4155901-0 s DE-604 Hamiltonsches System (DE-588)4139943-2 s Nichtintegrables System (DE-588)4462790-7 s Progress in mathematics 179 (DE-604)BV000004120 179 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008597374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Morales Ruiz, Juan J. Differential Galois theory and non-integrability of Hamiltonian systems Progress in mathematics Algèbre différentielle Algèbre différentielle ram Differentiaalvergelijkingen gtt Galois, Théorie de Galois, Théorie de ram Galois-theorie gtt Hamilton-vergelijkingen gtt Systèmes hamiltoniens Systèmes hamiltoniens ram Differential algebra Galois theory Hamiltonian systems Nichtintegrables System (DE-588)4462790-7 gnd Hamiltonsches System (DE-588)4139943-2 gnd Differentialalgebra (DE-588)4134657-9 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| subject_GND | (DE-588)4462790-7 (DE-588)4139943-2 (DE-588)4134657-9 (DE-588)4155901-0 |
| title | Differential Galois theory and non-integrability of Hamiltonian systems |
| title_auth | Differential Galois theory and non-integrability of Hamiltonian systems |
| title_exact_search | Differential Galois theory and non-integrability of Hamiltonian systems |
| title_full | Differential Galois theory and non-integrability of Hamiltonian systems Juan J. Morales Ruiz |
| title_fullStr | Differential Galois theory and non-integrability of Hamiltonian systems Juan J. Morales Ruiz |
| title_full_unstemmed | Differential Galois theory and non-integrability of Hamiltonian systems Juan J. Morales Ruiz |
| title_short | Differential Galois theory and non-integrability of Hamiltonian systems |
| title_sort | differential galois theory and non integrability of hamiltonian systems |
| topic | Algèbre différentielle Algèbre différentielle ram Differentiaalvergelijkingen gtt Galois, Théorie de Galois, Théorie de ram Galois-theorie gtt Hamilton-vergelijkingen gtt Systèmes hamiltoniens Systèmes hamiltoniens ram Differential algebra Galois theory Hamiltonian systems Nichtintegrables System (DE-588)4462790-7 gnd Hamiltonsches System (DE-588)4139943-2 gnd Differentialalgebra (DE-588)4134657-9 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| topic_facet | Algèbre différentielle Differentiaalvergelijkingen Galois, Théorie de Galois-theorie Hamilton-vergelijkingen Systèmes hamiltoniens Differential algebra Galois theory Hamiltonian systems Nichtintegrables System Hamiltonsches System Differentialalgebra Galois-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008597374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT moralesruizjuanj differentialgaloistheoryandnonintegrabilityofhamiltoniansystems |