Hamiltonian Dynamical Systems and Applications
Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical s...
Kaydedildi:
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| Diğer Yazarlar: | |
| Materyal Türü: | Livre numérique |
| Dil: | Anglais |
| Baskı/Yayın Bilgisi: |
Dordrecht :
Springer Netherlands
[20..].
Cham : Springer Nature |
| Edisyon: | 1st ed. 2008. |
| Seri Bilgileri: | NATO Science for Peace and Security Series B: Physics and Biophysics
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| Konular: | |
| Online Erişim: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Not: |
L'impression du document génère 449 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Variante du titre: | Proceedings of the NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications, Montreal, Canada, 18-29 June 2007 |
| Edition sous un autre format: | • Hamiltonian dynamical systems and applications, [proceedings of the NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications, Montreal, Canada, 18-29 June 2007], edited by Walter Craig,..., Dordrecht, Springer, 2008, 1 vol. (xv- 441 p.), NATO science for peace and security series, 978-1-4020-6962-8 |
| Özet: | Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems as well as the theory of Hamiltonian systems in infinite dimensional phase space; these are described in depth in this volume. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations. These lecture notes cover many areas of recent mathematical progress in this field, including the new choreographies of many body orbits, the development of rigorous averaging methods which give hope for realistic long time stability results, the development of KAM theory for partial differential equations in one and in higher dimensions, and the new developments in the long outstanding problem of Arnold diffusion. It also includes other contributions to celestial mechanics, to control theory, to partial differential equations of fluid dynamics, and to the theory of adiabatic invariants. In particular the last several years has seen major progress on the problems of KAM theory and Arnold diffusion; accordingly, this volume includes lectures on recent developments of KAM theory in infinite dimensional phase space, and descriptions of Arnold diffusion using variational methods as well as geometrical approaches to the gap problem. The subjects in question involve by necessity some of the most technical aspects of analysis coming from a number of diverse fields. Before the present volume, there has not been one text nor one course of study in which advanced students or experienced researchers from other areas can obtain an overview and background to enter this research area. This volume offers this, in an unparalleled series of extended lectures encompassing this wide spectrum of topics in PDE and dynamical systems |
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| Diğer Bilgileri: | L'impression du document génère 449 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliyografya: | Notes bibliogr. |
| ISBN: | 9781402069642 |
| ISSN: | 1874-6535 |
| Erişim: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |