Hamiltonian Systems with Three or More Degrees of Freedom:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1999
|
| Schriftenreihe: | NATO ASI Series, Series C:Mathematical and Physical Sciences
533 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions |
| Beschreibung: | 1 Online-Ressource (XXIV, 658 p) |
| ISBN: | 9789401146739 9789401059688 |
| ISSN: | 1389-2185 |
| DOI: | 10.1007/978-94-011-4673-9 |
Internformat
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| 245 | 1 | 0 | |a Hamiltonian Systems with Three or More Degrees of Freedom |c edited by Carles Simó |
| 246 | 1 | 3 | |a Proceedings of the NATO Advanced Study Institute, S'Agaro, Spain, June 19-30, 1995 |
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| 500 | |a A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions | ||
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Datensatz im Suchindex
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| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-94-011-4673-9 |
| format | Electronic eBook |
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| spelling | Simó, Carles Verfasser aut Hamiltonian Systems with Three or More Degrees of Freedom edited by Carles Simó Proceedings of the NATO Advanced Study Institute, S'Agaro, Spain, June 19-30, 1995 Dordrecht Springer Netherlands 1999 1 Online-Ressource (XXIV, 658 p) txt rdacontent c rdamedia cr rdacarrier NATO ASI Series, Series C:Mathematical and Physical Sciences 533 1389-2185 A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions Mathematics Global analysis Differential Equations Differential equations, partial Mechanics Global Analysis and Analysis on Manifolds Applications of Mathematics Ordinary Differential Equations Partial Differential Equations Mathematik Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1995 S'Agaro gnd-content Hamiltonsches System (DE-588)4139943-2 s 2\p DE-604 https://doi.org/10.1007/978-94-011-4673-9 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 | Simó, Carles Hamiltonian Systems with Three or More Degrees of Freedom Mathematics Global analysis Differential Equations Differential equations, partial Mechanics Global Analysis and Analysis on Manifolds Applications of Mathematics Ordinary Differential Equations Partial Differential Equations Mathematik Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4139943-2 (DE-588)1071861417 |
| title | Hamiltonian Systems with Three or More Degrees of Freedom |
| title_alt | Proceedings of the NATO Advanced Study Institute, S'Agaro, Spain, June 19-30, 1995 |
| title_auth | Hamiltonian Systems with Three or More Degrees of Freedom |
| title_exact_search | Hamiltonian Systems with Three or More Degrees of Freedom |
| title_full | Hamiltonian Systems with Three or More Degrees of Freedom edited by Carles Simó |
| title_fullStr | Hamiltonian Systems with Three or More Degrees of Freedom edited by Carles Simó |
| title_full_unstemmed | Hamiltonian Systems with Three or More Degrees of Freedom edited by Carles Simó |
| title_short | Hamiltonian Systems with Three or More Degrees of Freedom |
| title_sort | hamiltonian systems with three or more degrees of freedom |
| topic | Mathematics Global analysis Differential Equations Differential equations, partial Mechanics Global Analysis and Analysis on Manifolds Applications of Mathematics Ordinary Differential Equations Partial Differential Equations Mathematik Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Mathematics Global analysis Differential Equations Differential equations, partial Mechanics Global Analysis and Analysis on Manifolds Applications of Mathematics Ordinary Differential Equations Partial Differential Equations Mathematik Hamiltonsches System Konferenzschrift 1995 S'Agaro |
| url | https://doi.org/10.1007/978-94-011-4673-9 |
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