The Transition to Chaos: In Conservative Classical Systems: Quantum Manifestations
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1992
|
| Schriftenreihe: | Institute for Nonlinear Science
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | resonances. Nonlinear resonances cause divergences in conventional perturbation expansions. This occurs because nonlinear resonances cause a topological change locally in the structure of the phase space and simple perturbation theory is not adequate to deal with such topological changes. In Sect. (2.3), we introduce the concept of integrability. A sys tem is integrable if it has as many global constants of the motion as degrees of freedom. The connection between global symmetries and global constants of motion was first proven for dynamical systems by Noether [Noether 1918]. We will give a simple derivation of Noether's theorem in Sect. (2.3). As we shall see in more detail in Chapter 5, are whole classes of systems which are now known to be inte there grable due to methods developed for soliton physics. In Sect. (2.3), we illustrate these methods for the simple three-body Toda lattice. It is usually impossible to tell if a system is integrable or not just by looking at the equations of motion. The Poincare surface of section provides a very useful numerical tool for testing for integrability and will be used throughout the remainder of this book. We will illustrate the use of the Poincare surface of section for classic model of Henon and Heiles [Henon and Heiles 1964] |
| Beschreibung: | 1 Online-Ressource (XVI, 551 p) |
| ISBN: | 9781475743524 9781475743548 |
| ISSN: | 1431-4673 |
| DOI: | 10.1007/978-1-4757-4352-4 |
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| indexdate | 2024-07-10T01:20:50Z |
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| isbn | 9781475743524 9781475743548 |
| issn | 1431-4673 |
| language | English |
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| spelling | Reichl, L. E. Verfasser aut The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations by L. E. Reichl New York, NY Springer New York 1992 1 Online-Ressource (XVI, 551 p) txt rdacontent c rdamedia cr rdacarrier Institute for Nonlinear Science 1431-4673 resonances. Nonlinear resonances cause divergences in conventional perturbation expansions. This occurs because nonlinear resonances cause a topological change locally in the structure of the phase space and simple perturbation theory is not adequate to deal with such topological changes. In Sect. (2.3), we introduce the concept of integrability. A sys tem is integrable if it has as many global constants of the motion as degrees of freedom. The connection between global symmetries and global constants of motion was first proven for dynamical systems by Noether [Noether 1918]. We will give a simple derivation of Noether's theorem in Sect. (2.3). As we shall see in more detail in Chapter 5, are whole classes of systems which are now known to be inte there grable due to methods developed for soliton physics. In Sect. (2.3), we illustrate these methods for the simple three-body Toda lattice. It is usually impossible to tell if a system is integrable or not just by looking at the equations of motion. The Poincare surface of section provides a very useful numerical tool for testing for integrability and will be used throughout the remainder of this book. We will illustrate the use of the Poincare surface of section for classic model of Henon and Heiles [Henon and Heiles 1964] Physics Quantum theory Statistical Physics, Dynamical Systems and Complexity Quantum Information Technology, Spintronics Quantum Physics Quantentheorie https://doi.org/10.1007/978-1-4757-4352-4 Verlag Volltext |
| spellingShingle | Reichl, L. E. The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations Physics Quantum theory Statistical Physics, Dynamical Systems and Complexity Quantum Information Technology, Spintronics Quantum Physics Quantentheorie |
| title | The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations |
| title_auth | The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations |
| title_exact_search | The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations |
| title_full | The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations by L. E. Reichl |
| title_fullStr | The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations by L. E. Reichl |
| title_full_unstemmed | The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations by L. E. Reichl |
| title_short | The Transition to Chaos |
| title_sort | the transition to chaos in conservative classical systems quantum manifestations |
| title_sub | In Conservative Classical Systems: Quantum Manifestations |
| topic | Physics Quantum theory Statistical Physics, Dynamical Systems and Complexity Quantum Information Technology, Spintronics Quantum Physics Quantentheorie |
| topic_facet | Physics Quantum theory Statistical Physics, Dynamical Systems and Complexity Quantum Information Technology, Spintronics Quantum Physics Quantentheorie |
| url | https://doi.org/10.1007/978-1-4757-4352-4 |
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