Methods Of Hilbert Spaces In The Theory Of Nonlinear Dynamical Systems

Author : Krzysztof Kowalski
Publisher : World Scientific
ISBN 13 : 9789810217532
Total Pages : 148 pages
Book Rating : 4.36/5 ( download)

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Download or read book Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems written by Krzysztof Kowalski and published by World Scientific. This book was released on 1994 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schr”dinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the ?quantal? Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, B„cklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.

Author : Leon O Chua
Publisher : World Scientific
ISBN 13 : 9814494291
Total Pages : 591 pages
Book Rating : 4.98/5 ( download)

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Download or read book Methods Of Qualitative Theory In Nonlinear Dynamics (Part Ii) written by Leon O Chua and published by World Scientific. This book was released on 2001-09-27 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book has been written to serve that unfulfilled need.Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in the book have been developed only recently and have not yet appeared in textbook form.In keeping with the self-contained nature of the book, all the topics are developed with introductory background and complete mathematical rigor. Generously illustrated and written at a high level of exposition, this invaluable book will appeal to both the beginner and the advanced student of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.

Author : A.N. Leznov
Publisher : Birkhäuser
ISBN 13 : 9783034897099
Total Pages : 292 pages
Book Rating : 4.9X/5 ( download)

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Download or read book Group-Theoretical Methods for Integration of Nonlinear Dynamical Systems written by A.N. Leznov and published by Birkhäuser. This book was released on 2012-10-29 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews a large number of 1- and 2-dimensional equations that describe nonlinear phenomena in various areas of modern theoretical and mathematical physics. It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields. We hope that the book will be useful also for experts in hydrodynamics, solid-state physics, nonlinear optics electrophysics, biophysics and physics of the Earth. The first two chapters of the book present some results from the repre sentation theory of Lie groups and Lie algebras and their counterpart on supermanifolds in a form convenient in what follows. They are addressed to those who are interested in integrable systems but have a scanty vocabulary in the language of representation theory. The experts may refer to the first two chapters only occasionally. As we wanted to give the reader an opportunity not only to come to grips with the problem on the ideological level but also to integrate her or his own concrete nonlinear equations without reference to the literature, we had to expose in a self-contained way the appropriate parts of the representation theory from a particular point of view.

Author : A.N. Leznov
Publisher : Springer Science & Business Media
ISBN 13 : 9783764326159
Total Pages : 320 pages
Book Rating : 4.58/5 ( download)

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Download or read book Group-Theoretical Methods for Integration of Nonlinear Dynamical Systems written by A.N. Leznov and published by Springer Science & Business Media. This book was released on 1992-04-22 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews a large number of 1- and 2-dimensional equations that describe nonlinear phenomena in various areas of modern theoretical and mathematical physics. It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields. We hope that the book will be useful also for experts in hydrodynamics, solid-state physics, nonlinear optics electrophysics, biophysics and physics of the Earth. The first two chapters of the book present some results from the repre sentation theory of Lie groups and Lie algebras and their counterpart on supermanifolds in a form convenient in what follows. They are addressed to those who are interested in integrable systems but have a scanty vocabulary in the language of representation theory. The experts may refer to the first two chapters only occasionally. As we wanted to give the reader an opportunity not only to come to grips with the problem on the ideological level but also to integrate her or his own concrete nonlinear equations without reference to the literature, we had to expose in a self-contained way the appropriate parts of the representation theory from a particular point of view.

Author : Krzysztof Kowalski
Publisher : World Scientific
ISBN 13 : 9814506346
Total Pages : 192 pages
Book Rating : 4.42/5 ( download)

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Download or read book Nonlinear Dynamical Systems And Carleman Linearization written by Krzysztof Kowalski and published by World Scientific. This book was released on 1991-03-26 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Carleman linearization has become a new powerful tool in the study of nonlinear dynamical systems. Nevertheless, there is the general lack of familiarity with the Carleman embedding technique among those working in the field of nonlinear models. This book provides a systematic presentation of the Carleman linearization, its generalizations and applications. It also includes a review of existing alternative methods for linearization of nonlinear dynamical systems. There are probably no books covering such a wide spectrum of linearization algorithms. This book also gives a comprehensive introduction to the Kronecker product of matrices, whereas most books deal with it only superficially. The Kronecker product of matrices plays an important role in mathematics and in applications found in theoretical physics.

Author : Leonid P Shilnikov
Publisher : World Scientific
ISBN 13 : 9814496421
Total Pages : 416 pages
Book Rating : 4.21/5 ( download)

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Download or read book Methods of Qualitative Theory in Nonlinear Dynamics written by Leonid P Shilnikov and published by World Scientific. This book was released on 1998-12-08 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need. Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form. In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced students of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject. Contents:Basic ConceptsStructurally Stable Equilibrium States of Dynamical SystemsStructurally Stable Periodic Trajectories of Dynamical SystemsInvariant ToriCenter Manifold. Local CaseCenter Manifold. Non-Local Case Readership: Engineers, students, mathematicians and researchers in nonlinear dynamics and dynamical systems. Keywords:Bifurcations;Dynamical Systems;Qualitative Theory;Chaos;Strange Attractors;Nonlinear DynamicsReviews: “It is well-written and clearly organized with excellent figures … This rigorous book, with its emphasis on mathematical technique, would form an excellent basis for an engineering course if supplemented with applications.” Applied Mechanics Reviews “Short remarks concerning various, not only mathematical, aspects of the theory add an extra flavour to the text. I recommend the book for all persons interested in the qualitative theory of differential equations.” Mathematical Reviews

Author : Werner O. Amrein
Publisher : EPFL Press
ISBN 13 : 9781420066814
Total Pages : 416 pages
Book Rating : 4.11/5 ( download)

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Download or read book Hilbert Space Methods in Quantum Mechanics written by Werner O. Amrein and published by EPFL Press. This book was released on 2009-01-01 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The necessary foundation in quantum mechanics is covered in this book. Topics include basic properties of Hibert spaces, scattering theory, and a number of applications such as the S-matrix, time delay, and the Flux-Across-Surfaces Theorem.

Author : H.W. Broer
Publisher : Birkhäuser
ISBN 13 : 3034875185
Total Pages : 464 pages
Book Rating : 4.89/5 ( download)

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Download or read book Nonlinear Dynamical Systems and Chaos written by H.W. Broer and published by Birkhäuser. This book was released on 2013-11-11 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.

Author :
Publisher :
ISBN 13 :
Total Pages : 828 pages
Book Rating : 4.61/5 ( download)

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Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : S. Grivaux
Publisher : American Mathematical Soc.
ISBN 13 : 1470446634
Total Pages : 147 pages
Book Rating : 4.35/5 ( download)

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Download or read book Linear Dynamical Systems on Hilbert Spaces: Typical Properties and Explicit Examples written by S. Grivaux and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. (i) A typical hypercyclic operator is not topologically mixing, has no eigen-values and admits no non-trivial invariant measure, but is densely distri-butionally chaotic. (ii) A typical upper-triangular operator with coefficients of modulus 1 on the diagonal is ergodic in the Gaussian sense, whereas a typical operator of the form “diagonal with coefficients of modulus 1 on the diagonal plus backward unilateral weighted shift” is ergodic but has only countably many unimodular eigenvalues; in particular, it is ergodic but not ergodic in the Gaussian sense. (iii) There exist Hilbert space operators which are chaotic and U-frequently hypercyclic but not frequently hypercyclic, Hilbert space operators which are chaotic and frequently hypercyclic but not ergodic, and Hilbert space operators which are chaotic and topologically mixing but not U-frequently hypercyclic. We complement our results by investigating the descriptive complexity of some natural classes of operators defined by dynamical properties.