Symplectic Geometry of Integrable Hamiltonian Systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser Basel
2003
|
| Series: | Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemàtica
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. The quasi-periodicity of the solutions of an integrable system is a result of the fact that the system is invariant under a (semi-global) torus action. It is thus natural to investigate the symplectic manifolds that can be endowed with a (global) torus action. This leads to symplectic toric manifolds (Part B of this book). Physics makes a surprising come-back in Part A: to describe Mirror Symmetry, one looks for a special kind of Lagrangian submanifolds and integrable systems, the special Lagrangians. Furthermore, integrable Hamiltonian systems on punctured cotangent bundles are a starting point for the study of contact toric manifolds (Part C of this book) |
| Physical Description: | 1 Online-Ressource (240p) |
| ISBN: | 9783034880718 9783764321673 |
| DOI: | 10.1007/978-3-0348-8071-8 |
Staff View
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Record in the Search Index
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8071-8 |
| format | Electronic eBook |
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| spelling | Audin, Michèle Verfasser aut Symplectic Geometry of Integrable Hamiltonian Systems by Michèle Audin, Ana Cannas Silva, Eugene Lerman Basel Birkhäuser Basel 2003 1 Online-Ressource (240p) txt rdacontent c rdamedia cr rdacarrier Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemàtica Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. The quasi-periodicity of the solutions of an integrable system is a result of the fact that the system is invariant under a (semi-global) torus action. It is thus natural to investigate the symplectic manifolds that can be endowed with a (global) torus action. This leads to symplectic toric manifolds (Part B of this book). Physics makes a surprising come-back in Part A: to describe Mirror Symmetry, one looks for a special kind of Lagrangian submanifolds and integrable systems, the special Lagrangians. Furthermore, integrable Hamiltonian systems on punctured cotangent bundles are a starting point for the study of contact toric manifolds (Part C of this book) Mathematics Global differential geometry Cell aggregation / Mathematics Mathematical physics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Physics Mathematik Mathematische Physik Integrables System (DE-588)4114032-1 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 2001 Barcelona gnd-content Hamiltonsches System (DE-588)4139943-2 s Integrables System (DE-588)4114032-1 s Symplektische Geometrie (DE-588)4194232-2 s 2\p DE-604 Silva, Ana Cannas Sonstige oth Lerman, Eugene Sonstige oth https://doi.org/10.1007/978-3-0348-8071-8 Verlag Volltext 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 |
| spellingShingle | Audin, Michèle Symplectic Geometry of Integrable Hamiltonian Systems Mathematics Global differential geometry Cell aggregation / Mathematics Mathematical physics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Physics Mathematik Mathematische Physik Integrables System (DE-588)4114032-1 gnd Hamiltonsches System (DE-588)4139943-2 gnd Symplektische Geometrie (DE-588)4194232-2 gnd |
| subject_GND | (DE-588)4114032-1 (DE-588)4139943-2 (DE-588)4194232-2 (DE-588)1071861417 |
| title | Symplectic Geometry of Integrable Hamiltonian Systems |
| title_auth | Symplectic Geometry of Integrable Hamiltonian Systems |
| title_exact_search | Symplectic Geometry of Integrable Hamiltonian Systems |
| title_full | Symplectic Geometry of Integrable Hamiltonian Systems by Michèle Audin, Ana Cannas Silva, Eugene Lerman |
| title_fullStr | Symplectic Geometry of Integrable Hamiltonian Systems by Michèle Audin, Ana Cannas Silva, Eugene Lerman |
| title_full_unstemmed | Symplectic Geometry of Integrable Hamiltonian Systems by Michèle Audin, Ana Cannas Silva, Eugene Lerman |
| title_short | Symplectic Geometry of Integrable Hamiltonian Systems |
| title_sort | symplectic geometry of integrable hamiltonian systems |
| topic | Mathematics Global differential geometry Cell aggregation / Mathematics Mathematical physics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Physics Mathematik Mathematische Physik Integrables System (DE-588)4114032-1 gnd Hamiltonsches System (DE-588)4139943-2 gnd Symplektische Geometrie (DE-588)4194232-2 gnd |
| topic_facet | Mathematics Global differential geometry Cell aggregation / Mathematics Mathematical physics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Physics Mathematik Mathematische Physik Integrables System Hamiltonsches System Symplektische Geometrie Konferenzschrift 2001 Barcelona |
| url | https://doi.org/10.1007/978-3-0348-8071-8 |
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