Normal Forms and Stability of Hamiltonian Systems
This book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pe...
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| Format: | Électronique eBook |
| Langue: | anglais |
| Publié: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2023.
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| Édition: | 1st ed. 2023. |
| Collection: | Applied Mathematical Sciences,
218 |
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| Accès en ligne: | https://doi.org/10.1007/978-3-031-33046-9 |
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| 100 | 1 | |a Cabral, Hildeberto E. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Normal Forms and Stability of Hamiltonian Systems |h [electronic resource] / |c by Hildeberto E. Cabral, Lúcia Brandão Dias. |
| 250 | |a 1st ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online resource (XXI, 337 p. 29 illus.). |b 13 illus. in color. | ||
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| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
| 341 | 0 | |b Use of colour is Not sole means of conveying information |2 onix | |
| 341 | 0 | |b Use of high contrast between text and background colour |2 onix | |
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| 341 | 0 | |b All Non-decorative content supports reading without sight |2 onix | |
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| 490 | 1 | |a Applied Mathematical Sciences, |x 2196-968X ; |v 218 | |
| 505 | 0 | |a Foreword -- Preliminaries on Advanced Calculus -- Hamiltonian Systems Theory -- Normal Forms of Hamiltonian Systems -- Spectral Decomposition of Hamiltonian Matrices -- The General Linear Normalization -- Stability of Equilibria -- Stability of Linear Hamiltonian Systems -- Parametric Resonance -- References -- Index. | |
| 520 | |a This book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics. This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of strongly stable systems. With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
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| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Dynamical systems. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 1 | 4 | |a Dynamical Systems. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Mathematical Physics. |
| 700 | 1 | |a Brandão Dias, Lúcia. |e author. |0 (orcid)0000-0002-2546-0658 |1 https://orcid.org/0000-0002-2546-0658 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 830 | 0 | |a Applied Mathematical Sciences, |x 2196-968X ; |v 218 | |
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