Notes on Hamiltonian dynamical systems:
Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov-Arnold-Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows stude...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2022
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| Schriftenreihe: | London Mathematical Society student texts
102 |
| Schlagworte: | |
| Online-Zugang: | BSB01 BTU01 FHN01 UBM01 URL des Erstveröffentlichers |
| Zusammenfassung: | Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov-Arnold-Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincaré's non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincaré and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 07 Apr 2022) |
| Beschreibung: | 1 Online-Ressource (xix, 451 Seiten) |
| ISBN: | 9781009151122 |
| DOI: | 10.1017/9781009151122 |
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| index_date | 2024-07-03T19:54:04Z |
| indexdate | 2024-07-10T09:32:51Z |
| institution | BVB |
| isbn | 9781009151122 |
| language | English |
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| spelling | Giorgilli, Antonio 1949- (DE-588)1258279614 aut Notes on Hamiltonian dynamical systems Antonio Giorgilli, University of Milan Cambridge Cambridge University Press 2022 1 Online-Ressource (xix, 451 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society student texts 102 Title from publisher's bibliographic system (viewed on 07 Apr 2022) Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov-Arnold-Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincaré's non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincaré and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students Hamiltonian systems Systemanalyse (DE-588)4116673-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Dynamisches System (DE-588)4013396-5 s Systemanalyse (DE-588)4116673-5 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-00-915114-6 https://doi.org/10.1017/9781009151122 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Giorgilli, Antonio 1949- Notes on Hamiltonian dynamical systems Hamiltonian systems Systemanalyse (DE-588)4116673-5 gnd Dynamisches System (DE-588)4013396-5 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4116673-5 (DE-588)4013396-5 (DE-588)4139943-2 |
| title | Notes on Hamiltonian dynamical systems |
| title_auth | Notes on Hamiltonian dynamical systems |
| title_exact_search | Notes on Hamiltonian dynamical systems |
| title_exact_search_txtP | Notes on Hamiltonian dynamical systems |
| title_full | Notes on Hamiltonian dynamical systems Antonio Giorgilli, University of Milan |
| title_fullStr | Notes on Hamiltonian dynamical systems Antonio Giorgilli, University of Milan |
| title_full_unstemmed | Notes on Hamiltonian dynamical systems Antonio Giorgilli, University of Milan |
| title_short | Notes on Hamiltonian dynamical systems |
| title_sort | notes on hamiltonian dynamical systems |
| topic | Hamiltonian systems Systemanalyse (DE-588)4116673-5 gnd Dynamisches System (DE-588)4013396-5 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Hamiltonian systems Systemanalyse Dynamisches System Hamiltonsches System |
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