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Author: P.R. Chernoff
Publisher:
ISBN: 9783662211823
Category :
Languages : en
Pages : 172
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Book Description
Author: P.R. Chernoff
Publisher:
ISBN: 9783662211823
Category :
Languages : en
Pages : 172
Get Book Here
Book Description
Author: Paul R. Chernoff
Publisher:
ISBN:
Category : Dynamics
Languages : en
Pages : 160
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Book Description
Author: Paul R. Chernoff
Publisher:
ISBN:
Category :
Languages : de
Pages :
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Book Description
Author: P.R. Chernoff
Publisher: Springer
ISBN: 3540372873
Category : Mathematics
Languages : en
Pages : 165
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Book Description
Author: Sergej B. Kuksin
Publisher: Springer
ISBN: 3540479201
Category : Mathematics
Languages : en
Pages : 128
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Book Description
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:
ISBN:
Category : Hamiltonian systems
Languages : en
Pages :
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Book Description
Author: Rudolf Schmid
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 178
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Book Description
Author: Birgit Jacob
Publisher: Springer Science & Business Media
ISBN: 3034803990
Category : Science
Languages : en
Pages : 221
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Book Description
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: George Isaac Hagstrom
Publisher:
ISBN:
Category :
Languages : en
Pages : 244
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Book Description
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.
Author: Wilfrid Gangbo
Publisher: American Mathematical Soc.
ISBN: 0821849395
Category : Mathematics
Languages : en
Pages : 90
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Book Description
Let $\mathcal{M}$ denote the space of probability measures on $\mathbb{R}^D$ endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely continuous curves in $\mathcal{M}$ was introduced by Ambrosio, Gigli, and Savare. In this paper the authors develop a calculus for the corresponding class of differential forms on $\mathcal{M}$. In particular they prove an analogue of Green's theorem for 1-forms and show that the corresponding first cohomology group, in the sense of de Rham, vanishes. For $D=2d$ the authors then define a symplectic distribution on $\mathcal{M}$ in terms of this calculus, thus obtaining a rigorous framework for the notion of Hamiltonian systems as introduced by Ambrosio and Gangbo. Throughout the paper the authors emphasize the geometric viewpoint and the role played by certain diffeomorphism groups of $\mathbb{R}^D$.
