Properties of Infinite Dimensional Hamiltonian Systems
Author : P.R. Chernoff
Publisher :
Page : 172 pages
File Size : 37,52 MB
Release : 2014-06-18
Category :
ISBN : 9783662211823
Author : P.R. Chernoff
Publisher :
Page : 172 pages
File Size : 37,52 MB
Release : 2014-06-18
Category :
ISBN : 9783662211823
Author : Paul R. Chernoff
Publisher :
Page : 160 pages
File Size : 35,79 MB
Release : 1974
Category : Dynamics
ISBN :
Author : Paul R. Chernoff
Publisher :
Page : pages
File Size : 44,13 MB
Release : 1974
Category :
ISBN :
Author : P.R. Chernoff
Publisher : Springer
Page : 165 pages
File Size : 25,23 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540372873
Author : Sergej B. Kuksin
Publisher : Springer
Page : 128 pages
File Size : 39,72 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540479201
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.
Author : Julia Theresa Kaiser
Publisher :
Page : pages
File Size : 22,83 MB
Release : 2021
Category : Hamiltonian systems
ISBN :
Author : Rudolf Schmid
Publisher :
Page : 178 pages
File Size : 22,62 MB
Release : 1987
Category : Science
ISBN :
Author : Birgit Jacob
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 39,12 MB
Release : 2012-06-13
Category : Science
ISBN : 3034803990
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.
Author : Hideki Omori
Publisher :
Page : 280 pages
File Size : 38,80 MB
Release : 1974
Category : Algebraic topology
ISBN : 9780387070117
Author : George Isaac Hagstrom
Publisher :
Page : 244 pages
File Size : 29,15 MB
Release : 2011
Category :
ISBN :
Various properties of linear infinite-dimensional Hamiltonian systems are studied. The structural stability of the Vlasov-Poisson equation linearized around a homogeneous stable equilibrium [mathematical symbol] is investigated in a Banach space setting. It is found that when perturbations of [mathematical symbols] are allowed to live in the space [mathematical symbols], every equilibrium is structurally unstable. When perturbations are restricted to area preserving rearrangements of [mathematical symbol], structural stability exists if and only if there is negative signature in the continuous spectrum. This analogizes Krein's theorem for linear finite-dimensional Hamiltonian systems. The techniques used to prove this theorem are applied to other aspects of the linearized Vlasov-Poisson equation, in particular the energy of discrete modes which are embedded within the continuous spectrum. In the second part, an integral transformation that exactly diagonalizes the Caldeira-Leggett model is presented. The resulting form of the Hamiltonian, derived using canonical transformations, is shown to be identical to that of the linearized Vlasov-Poisson equation. The damping mechanism in the Caldeira-Leggett model is identified with the Landau damping of a plasma. The correspondence between the two systems suggests the presence of an echo effect in the Caldeira-Leggett model. Generalizations of the Caldeira-Leggett model with negative energy are studied and interpreted in the context of Krein's theorem.