Nearly Integrable Infinite Dimensional Hamiltonian Systems
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Nearly Integrable Infinite Dimensional Hamiltonian Systems
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Author : Sergej B. Kuksin
language : en
Publisher:
Release Date : 2014-01-15
Nearly Integrable Infinite Dimensional Hamiltonian Systems written by Sergej B. Kuksin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Nearly Integrable Infinite Dimensional Hamiltonian Systems
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Author : Sergej B. Kuksin
language : en
Publisher: Springer
Release Date : 2006-11-15
Nearly Integrable Infinite Dimensional Hamiltonian Systems written by Sergej B. Kuksin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The book is devoted to partial differential equations of Hamiltonian form, close to integrable equations. For such equations a KAM-like theorem is proved, stating that solutions of the unperturbed equation that are quasiperiodic in time mostly persist in the perturbed one. The theorem is applied to classical nonlinear PDE's with one-dimensional space variable such as the nonlinear string and nonlinear Schr|dinger equation andshow that the equations have "regular" (=time-quasiperiodic and time-periodic) solutions in rich supply. These results cannot be obtained by other techniques. The book will thus be of interest to mathematicians and physicists working with nonlinear PDE's. An extensivesummary of the results and of related topics is provided in the Introduction. All the nontraditional material used is discussed in the firstpart of the book and in five appendices.
Quasiperiodic Solutions Of Nearly Integrable Infinite Dimensional Hamiltonian Systems
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Author : S. B. Kuksin
language : de
Publisher:
Release Date : 1991
Quasiperiodic Solutions Of Nearly Integrable Infinite Dimensional Hamiltonian Systems written by S. B. Kuksin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
Quasiperiodic Solutions Of Nearly Integrable Infinite Dimensional Hamiltonian Systems
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Author : Sergei B. Kuksin
language : en
Publisher:
Release Date : 1991
Quasiperiodic Solutions Of Nearly Integrable Infinite Dimensional Hamiltonian Systems written by Sergei B. Kuksin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
Stochastic Pde S And Kolmogorov Equations In Infinite Dimensions
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Author : N.V. Krylov
language : en
Publisher: Springer
Release Date : 2006-11-15
Stochastic Pde S And Kolmogorov Equations In Infinite Dimensions written by N.V. Krylov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.
Variational And Local Methods In The Study Of Hamiltonian Systems Proceedings Of The Workshop
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Author : Antonio Ambrosetti
language : en
Publisher: World Scientific
Release Date : 1995-09-30
Variational And Local Methods In The Study Of Hamiltonian Systems Proceedings Of The Workshop written by Antonio Ambrosetti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-30 with categories.
In this volume, various ideas about Hamiltonian dynamics were discussed. Particular emphasis was placed on mechanical systems with singular potentials (such as the N-Body Newtonian problem) and on their special features, although important aspects of smooth dynamics were also discussed, from both the local point of view and the point of view of global analysis.
Hamiltonian Dynamical Systems And Applications
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Author : Walter Craig
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-17
Hamiltonian Dynamical Systems And Applications written by Walter Craig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-17 with Mathematics categories.
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. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
Analysis Of Hamiltonian Pdes
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Author : Sergej B. Kuksin
language : en
Publisher: Clarendon Press
Release Date : 2000
Analysis Of Hamiltonian Pdes written by Sergej B. Kuksin and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
For the last 20-30 years, interest among mathematicians and physicists in infinite-dimensional Hamiltonian systems and Hamiltonian partial differential equations has been growing strongly, and many papers and a number of books have been written on integrable Hamiltonian PDEs. During the last decade though, the interest has shifted steadily towards non-integrable Hamiltonian PDEs. Here, not algebra but analysis and symplectic geometry are the appropriate analysing tools. The present book is the first one to use this approach to Hamiltonian PDEs and present a complete proof of the "KAM for PDEs" theorem. It will be an invaluable source of information for postgraduate mathematics and physics students and researchers.
Nonlinear Oscillations Of Hamiltonian Pdes
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Author : Massimiliano Berti
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-01
Nonlinear Oscillations Of Hamiltonian Pdes written by Massimiliano Berti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-01 with Mathematics categories.
Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. The text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.