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Titlebook: Hamiltonian Dynamical Systems and Applications; Walter Craig Conference proceedings 20081st edition Springer Science+Business Media B.V. 2

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发表于 2025-3-21 18:03:10 | 显示全部楼层 |阅读模式
书目名称Hamiltonian Dynamical Systems and Applications
编辑Walter Craig
视频video
概述Lecture notes on current state-of-the-art by the researchers who have developed the theory.Introductions of the technically deep methods of Hamiltonian mechanics to partial differential equations.Cont
丛书名称NATO Science for Peace and Security Series B: Physics and Biophysics
图书封面Titlebook: Hamiltonian Dynamical Systems and Applications;  Walter Craig Conference proceedings 20081st edition Springer Science+Business Media B.V. 2
描述.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
出版日期Conference proceedings 20081st edition
关键词Biophysics; NATO; Physics; Potential; Science; Security; Sobolev space; Sub-Series B; analysis; partial diffe
版次1
doihttps://doi.org/10.1007/978-1-4020-6964-2
isbn_softcover978-1-4020-6963-5
isbn_ebook978-1-4020-6964-2Series ISSN 1874-6500 Series E-ISSN 1874-6535
issn_series 1874-6500
copyrightSpringer Science+Business Media B.V. 2008
The information of publication is updating

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https://doi.org/10.1007/978-1-4684-5353-9t motions. Adiabatic perturbation theory is a mathematical tool for the asymptotic description of dynamics in such systems. This theory allows to construct adiabatic invariants, which are approximate first integrals of the systems. These quantities change by small amounts on large time intervals, ov
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https://doi.org/10.1007/978-94-017-5914-4by a procedure that is a geometric elaboration of the Lagrange multipliers rule. The intimate relation of the optimal control and Hamiltonian dynamics is fruitful for both domains; among other things, it leads to a clarification and a far going generalization of important classical results about Rie
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https://doi.org/10.1007/978-94-015-7243-9finite dimensions, where the second Melnikov’s conditions are completely eliminated and the algebraic structure of the normal frequencies is not required. This theorem can be used to construct invariant tori and quasi-periodic solutions for nonlinear wave equations, Schrödinger equations and other e
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The Phylogenetic System of Ephemeropteratial in dimension .. Central in this theory is the homological equation and a condition on the small divisors often known as the second Melnikov condition. The difficulties related to this condition are substantial when .≥ 2..We discuss this difficulty, and we show that a block decomposition and a T
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The Physical Attractiveness Phenomenatablish the presence of these structures in a given near integrable systems or in systems for which good numerical information is available. We also discuss some quantitative features of the diffusion mechanisms such as time of diffusion, Hausdorff dimension of diffusing orbits, etc.
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