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Author : P.R. Chernoff
Publisher :
ISBN 13 : 9783662211823
Total Pages : 172 pages
Book Rating : 4.2/5 (118 download)
Download or read book Properties of Infinite Dimensional Hamiltonian Systems written by P.R. Chernoff and published by . This book was released on 2014-06-18 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul R. Chernoff
Publisher :
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.:/5 (1 download)
Download or read book Properties of Infinite Dimensional Hamiltonian Systems written by Paul R. Chernoff and published by . This book was released on 1974 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul R. Chernoff
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (471 download)
Download or read book Properties of infinite dimensional Hamiltonian systems written by Paul R. Chernoff and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P.R. Chernoff
Publisher : Springer
ISBN 13 : 3540372873
Total Pages : 165 pages
Book Rating : 4.5/5 (43 download)
Download or read book Properties of Infinite Dimensional Hamiltonian Systems written by P.R. Chernoff and published by Springer. This book was released on 2006-11-15 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sergej B. Kuksin
Publisher : Springer
ISBN 13 : 3540479201
Total Pages : 128 pages
Book Rating : 4.5/5 (44 download)
Download or read book Nearly Integrable Infinite-Dimensional Hamiltonian Systems written by Sergej B. Kuksin and published by Springer. This book was released on 2006-11-15 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 :
Total Pages : pages
Book Rating : 4.:/5 (124 download)
Download or read book System Theoretical Properties of Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces written by Julia Theresa Kaiser and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rudolf Schmid
Publisher :
ISBN 13 :
Total Pages : 178 pages
Book Rating : 4.3/5 (91 download)
Download or read book Infinite Dimensional Hamiltonian Systems written by Rudolf Schmid and published by . This book was released on 1987 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Birgit Jacob
Publisher : Springer Science & Business Media
ISBN 13 : 3034803990
Total Pages : 221 pages
Book Rating : 4.0/5 (348 download)
Download or read book Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces written by Birgit Jacob and published by Springer Science & Business Media. This book was released on 2012-06-13 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
ISBN 13 : 9780387070117
Total Pages : 280 pages
Book Rating : 4.0/5 (71 download)
Download or read book Algebraic and Geometrical Methods in Topology written by Hideki Omori and published by . This book was released on 1974 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : George Isaac Hagstrom
Publisher :
ISBN 13 :
Total Pages : 244 pages
Book Rating : 4.:/5 (758 download)
Download or read book Infinite-dimensional Hamiltonian Systems with Continuous Spectra written by George Isaac Hagstrom and published by . This book was released on 2011 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 0821849395
Total Pages : 90 pages
Book Rating : 4.8/5 (218 download)
Download or read book Differential Forms on Wasserstein Space and Infinite-Dimensional Hamiltonian Systems written by Wilfrid Gangbo and published by American Mathematical Soc.. This book was released on 2010 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 $\mathbb{R}^D$.
Author : Alexander Mielke
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (52 download)
Download or read book Dispersive Stability of Infinite Dimensional Hamiltonian Systems on Lattices written by Alexander Mielke and published by . This book was released on 2009 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Joachim Kerner
Publisher : Springer Nature
ISBN 13 : 3030358984
Total Pages : 194 pages
Book Rating : 4.0/5 (33 download)
Download or read book Control Theory of Infinite-Dimensional Systems written by Joachim Kerner and published by Springer Nature. This book was released on 2020-06-25 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents novel results by participants of the conference “Control theory of infinite-dimensional systems” that took place in January 2018 at the FernUniversität in Hagen. Topics include well-posedness, controllability, optimal control problems as well as stability of linear and nonlinear systems, and are covered by world-leading experts in these areas. A distinguishing feature of the contributions in this volume is the particular combination of researchers from different fields in mathematics working in an interdisciplinary fashion on joint projects in mathematical system theory. More explicitly, the fields of partial differential equations, semigroup theory, mathematical physics, graph and network theory as well as numerical analysis are all well-represented.
Author : Jerrold E. Marsden
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (174 download)
Download or read book Hamiltonian One Parameter Groups written by Jerrold E. Marsden and published by . This book was released on 1969* with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wilfrid Gangbo
Publisher :
ISBN 13 : 9781470406103
Total Pages : 77 pages
Book Rating : 4.4/5 (61 download)
Download or read book Differential Forms on Wasserstein Space and Infinite-dimensional Hamiltonian Systems written by Wilfrid Gangbo and published by . This book was released on 2010 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Basil Nicolaenko
Publisher : American Mathematical Soc.
ISBN 13 : 0821851055
Total Pages : 380 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Connection between Infinite Dimensional and Finite Dimensional Dynamical Systems written by Basil Nicolaenko and published by American Mathematical Soc.. This book was released on 1989 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last few years have seen a number of major developments demonstrating that the long-term behavior of solutions of a very large class of partial differential equations possesses a striking resemblance to the behavior of solutions of finite dimensional dynamical systems, or ordinary differential equations. The first of these advances was the discovery that a dissipative PDE has a compact, global attractor with finite Hausdorff and fractal dimensions. More recently, it was shown that some of these PDEs possess a finite dimensional inertial manifold-that is, an invariant manifold containing the attractor and exponentially attractive trajectories. With the improved understanding of the exact connection between finite dimensional dynamical systems and various classes of dissipative PDEs, it is now realistic to hope that the wealth of studies of such topics as bifurcations of finite vector fields and ``strange'' fractal attractors can be brought to bear on various mathematical models, including continuum flows. Surprisingly, a number of distributed systems from continuum mechanics have been found to exhibit the same nontrivial dynamic behavior as observed in low-dimensional dynamical systems. As a natural consequence of these observations, a new direction of research has arisen: detection and analysis of finite dimensional dynamical characteristics of infinite-dimensional systems. This book represents the proceedings of an AMS-IMS-SIAM Summer Research Conference, held in July, 1987 at the University of Colorado at Boulder. Bringing together mathematicians and physicists, the conference provided a forum for presentations on the latest developments in the field and fostered lively interactions on open questions and future directions. With contributions from some of the top experts, these proceedings will provide readers with an overview of this vital area of research.
Author : Russell Johnson
Publisher : Springer
ISBN 13 : 3319290258
Total Pages : 515 pages
Book Rating : 4.3/5 (192 download)
Download or read book Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control written by Russell Johnson and published by Springer. This book was released on 2016-03-25 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense. The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory.
