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Attractive Invariant Manifolds Under Approximation Part I Inertial Manifolds
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Book Synopsis Approximation of Stochastic Invariant Manifolds by : Mickaël D. Chekroun
Download or read book Approximation of Stochastic Invariant Manifolds written by Mickaël D. Chekroun and published by Springer. This book was released on 2014-12-20 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.
Book Synopsis Multiple Time Scale Dynamics by : Christian Kuehn
Download or read book Multiple Time Scale Dynamics written by Christian Kuehn and published by Springer. This book was released on 2015-02-25 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Book Synopsis Dynamical Systems and Numerical Analysis by : Andrew Stuart
Download or read book Dynamical Systems and Numerical Analysis written by Andrew Stuart and published by Cambridge University Press. This book was released on 1998-11-28 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.
Book Synopsis Numerical Analysis 1993 by : D.F. Griffiths
Download or read book Numerical Analysis 1993 written by D.F. Griffiths and published by CRC Press. This book was released on 2020-10-08 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited papers presented at the 15th Dundee Biennial Conference on Numerical Analysis held at the University of Dundee in June of 1993. The Dundee Conferences are important events in the numerical analysis calendar, and the papers published here represent accounts of recent research work by leading numerical analysts covering a wide range of fields of interest. The book is a valuable guide to the direction of current research in many areas of numerical analysis. It will be of particular interest to graduate students and research workers concerned with the theory and application of numerical methods for solving ordinary and partial differential equations.
Author :Alexander N. Gorban Publisher :Springer Science & Business Media ISBN 13 :9783540226840 Total Pages :524 pages Book Rating :4.2/5 (268 download)
Book Synopsis Invariant Manifolds for Physical and Chemical Kinetics by : Alexander N. Gorban
Download or read book Invariant Manifolds for Physical and Chemical Kinetics written by Alexander N. Gorban and published by Springer Science & Business Media. This book was released on 2005-02-01 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: By bringing together various ideas and methods for extracting the slow manifolds, the authors show that it is possible to establish a more macroscopic description in nonequilibrium systems. The book treats slowness as stability. A unifying geometrical viewpoint of the thermodynamics of slow and fast motion enables the development of reduction techniques, both analytical and numerical. Examples considered in the book range from the Boltzmann kinetic equation and hydrodynamics to the Fokker-Planck equations of polymer dynamics and models of chemical kinetics describing oxidation reactions. Special chapters are devoted to model reduction in classical statistical dynamics, natural selection, and exact solutions for slow hydrodynamic manifolds. The book will be a major reference source for both theoretical and applied model reduction. Intended primarily as a postgraduate-level text in nonequilibrium kinetics and model reduction, it will also be valuable to PhD students and researchers in applied mathematics, physics and various fields of engineering.
Book Synopsis Indiana University Mathematics Journal by : Indiana University. Dept. of Mathematics
Download or read book Indiana University Mathematics Journal written by Indiana University. Dept. of Mathematics and published by . This book was released on 2001 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Acta Numerica 1994: Volume 3 by : Arieh Iserles
Download or read book Acta Numerica 1994: Volume 3 written by Arieh Iserles and published by Cambridge University Press. This book was released on 1994-07-29 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acta Numerica is an annual volume presenting survey papers in numerical analysis accessible to graduate students and researchers. Highlights of the 1994 issue are articles on domain decomposition, mesh adaption, pseudospectral methods and neural networks.
Book Synopsis Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by : Bernold Fiedler
Download or read book Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems written by Bernold Fiedler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.
Book Synopsis Nonautonomous Dynamical Systems by : Peter E. Kloeden
Download or read book Nonautonomous Dynamical Systems written by Peter E. Kloeden and published by American Mathematical Soc.. This book was released on 2011-08-17 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.
Book Synopsis Geometric Theory of Discrete Nonautonomous Dynamical Systems by : Christian Pötzsche
Download or read book Geometric Theory of Discrete Nonautonomous Dynamical Systems written by Christian Pötzsche and published by Springer Science & Business Media. This book was released on 2010-09-17 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).
Book Synopsis Attractors and Inertial Manifolds by : Boling Guo
Download or read book Attractors and Inertial Manifolds written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-07-09 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold
Book Synopsis Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations by : Mickaël D. Chekroun
Download or read book Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations written by Mickaël D. Chekroun and published by Springer. This book was released on 2014-12-23 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
Book Synopsis Effective Dynamics of Stochastic Partial Differential Equations by : Jinqiao Duan
Download or read book Effective Dynamics of Stochastic Partial Differential Equations written by Jinqiao Duan and published by Elsevier. This book was released on 2014-03-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. - New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty - Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations - Solutions or hints to all Exercises
Book Synopsis Featured Reviews in "Mathematical Reviews" 1995-1996 by : Donald G. Babbitt
Download or read book Featured Reviews in "Mathematical Reviews" 1995-1996 written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of reprinted 'Featured Reviews' published in Mathematical Reviews (MR) in 1995 and 1996 makes widely available informed reviews of some of the best mathematics published recently. 'Featured Reviews' were introduced in MR at the beginning of 1995 in part to provide some guidance to the current research-level literature. With the exponential growth of publications in mathematical research in the first half-century of MR, it had become essentially impossible for users of MR to identify the most important new research-level books and papers, especially in fields outside of the users' own expertise. This work identifies some of the "best" new publications, papers, and books that are expected to have a significant impact on the area of pure or applied mathematics with which researchers are concerned. All of the papers reviewed here contain interesting new ideas or applications, a deep synthesis of existing ideas, or any combination of these. The volume is intended to lead the user to important new research across all fields covered by MR.
Book Synopsis Classical Mechanics by : Joseph L. McCauley
Download or read book Classical Mechanics written by Joseph L. McCauley and published by Cambridge University Press. This book was released on 1997-05-08 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced text is the first book to describe the subject of classical mechanics in the context of the language and methods of modern nonlinear dynamics. The organizing principle of the text is integrability vs. nonintegrability.
Book Synopsis The Connection between Infinite Dimensional and Finite Dimensional Dynamical Systems by : Basil Nicolaenko
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.
Download or read book CMUC written by and published by . This book was released on 1995 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt:
