Download or read book Nearly Integrable Infinite Dimensional Hamiltonian Systems written by Sergej B. Kuksin and published by . This book was released on 2014-01-15 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Infinite Dimensional Dynamical Systems written by John Mallet-Paret and published by Springer Science & Business Media. This book was released on 2012-10-11 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation and applications of new developments of nonlinear analysis and other mathematical theories. Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects the pioneering work and influence of Professor Sell in a few core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.
Download or read book Potential Theory on Infinite Networks written by Paolo M. Soardi and published by Springer. This book was released on 2006-11-15 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds. The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.
Download or read book Hamiltonian Mechanics written by John Seimenis and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited papers and contributions delivered at the International Conference on Hamiltonian Mechanics: Integrability and Chaotic Behaviour, held in Tornn, Poland during the summer of 1993. The conference was supported by the NATO Scientific and Environmental Affairs Division as an Advanced Research Workshop. In fact, it was the first scientific conference in all Eastern Europe supported by NATO. The meeting was expected to establish contacts between East and West experts as well as to study the current state of the art in the area of Hamiltonian Mechanics and its applications. I am sure that the informal atmosphere of the city of Torun, the birthplace of Nicolaus Copernicus, stimulated many valuable scientific exchanges. The first idea for this cnference was carried out by Prof Andrzej J. Maciejewski and myself, more than two years ago, during his visit in Greece. It was planned for about forty well-known scientists from East and West. At that time participation of a scientist from Eastern Europe in an Organising Committee of a NATO Conference was not allowed. But always there is the first time. Our plans for such a "small" conference, as a first attempt in the new European situation -the Europe without borders -quickly passed away. The names of our invited speakers, authorities in their field, were a magnet for many colleagues from all over the world.
Download or read book Dynamical Systems and Probabilistic Methods in Partial Differential Equations written by Percy Deift and published by American Mathematical Soc.. This book was released on 1996 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains some of the lectures presented in June 1994 during the AMS-SIAM Summer Seminar at the Mathematical Sciences Research Institute in Berkeley. The goal of the seminar was to introduce participants to as many interesting and active applications of dynamical systems and probabilistic methods to problems in applied mathematics as possible. As a result, this book covers a great deal of ground. Nevertheless, the pedagogical orientation of the lectures has been retained, and therefore the book will serve as an ideal introduction to these varied and interesting topics.
Download or read book Control Theory And Related Topics In Memory Of Professor Xunjing Li written by Shanjian Tang and published by World Scientific. This book was released on 2007-09-27 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Xunjing Li (1935-2003) was a pioneer in control theory in China. He was known in the Chinese community of applied mathematics, and in the global community of optimal control theory of distributed parameter systems. He has made important contributions to the optimal control theory of distributed parameter systems, in particular regarding the first-order necessary conditions (Pontryagin-type maximum principle) for optimal control of nonlinear infinite-dimensional systems. He directed the Seminar of Control Theory at Fudan towards stochastic control theory in 1980s, and mathematical finance in 1990s, which has led to several important subsequent developments in both closely interactive fields. These remarkable efforts in scientific research and education, among others, gave birth to the so-called “Fudan School”.This proceedings volume includes a collection of original research papers or reviews authored or co-authored by Xunjing Li's former students, postdoctoral fellows, and mentored scholars in the areas of control theory, dynamic systems, mathematical finance, and stochastic analysis, among others.
Download or read book Control Theory and Related Topics written by Shanjian Tang and published by World Scientific. This book was released on 2007 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Xunjing Li (1935OCo2003) was a pioneer in control theory in China. He was known in the Chinese community of applied mathematics, and in the global community of optimal control theory of distributed parameter systems. He has made important contributions to the optimal control theory of distributed parameter systems, in particular regarding the first-order necessary conditions (Pontryagin-type maximum principle) for optimal control of nonlinear infinite-dimensional systems. He directed the Seminar of Control Theory at Fudan towards stochastic control theory in 1980s, and mathematical finance in 1990s, which has led to several important subsequent developments in both closely interactive fields. These remarkable efforts in scientific research and education, among others, gave birth to the so-called OC Fudan SchoolOCO. This proceedings volume includes a collection of original research papers or reviews authored or co-authored by Xunjing Li''s former students, postdoctoral fellows, and mentored scholars in the areas of control theory, dynamic systems, mathematical finance, and stochastic analysis, among others. Sample Chapter(s). Part 1: A Tribute in Memory of Professor Xunjing Li on His Seventieth Birthday (112 KB). Contents: Stochastic Control, Mathematical Finance, and Backward Stochastic Differential Equations: Axiomatic Characteristics for Solutions of Reflected Backward Stochastic Differential Equations (X Bao & S Tang); A Linear Quadratic Optimal Control Problem for Stochastic Volterra Integral Equations (S Chen & J Yong); Stochastic Control and BSDEs with Quadratic Growth (M Fuhrman et al.); Unique Continuation and Observability for Stochastic Parabolic Equations and Beyond (X Zhang); Deterministic Control Systems: Some Counterexamples in Existence Theory of Optimal Control (H Lou); A Generalized Framework for Global Output Feedback Stabilization of Inherently Nonlinear Systems with Uncertainties (J Polendo & C Qian); On Finite-Time Stabilization of a Class of Nonsmoothly Stabilizable Systems (B Yang & W Lin); Dynamics and Optimal Control of Partial Differential Equations: Optimal Control of Quasilinear Elliptic Obstacle Problems (Q Chen & Y Ye); Controllability of a Nonlinear Degenerate Parabolic System with Bilinear Control (P Lin et al.); and other papers. Readership: Researchers and graduate students in the areas of control theory, mathematical finance and dynamical systems."
Download or read book Journal of Fourier Analysis and Applications Special Issue written by John J. Benedetto and published by CRC Press. This book was released on 2020-03-10 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Journal of Fourier Analysis and Applications is a journal of the mathematical sciences devoted to Fourier analysis and its applications. The subject of Fourier analysis has had a major impact on the development of mathematics, on the understanding of many engineering and scientific phenomena, and on the solution of some of the most important problems in mathematics and the sciences. At the end of June 1993, a large Conference in Harmonic Analysis was held at the University of Paris-Sud at Orsay to celebrate the prominent role played by Jean-Pierre Kahane and his numerous achievements in this field. The large variety of topics discussed in this meeting, ranging from classical Harmonic Analysis to Probability Theory, reflects the intense mathematical curiosity and the broad mathematical interest of Jean-Pierre Kahane. Indeed, all of them are connected to his work. The mornings were devoted to plenary addresses while up to four parallel sessions took place in the afternoons. Altogether, there were about eighty speakers. This wide range of subjects appears in these proceedings which include thirty six articles.
Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Download or read book Stability of KAM Tori for Nonlinear Schr dinger Equation written by Hongzi Cong and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove the long time stability of KAM tori (thus quasi-periodic solutions) for nonlinear Schrödinger equation subject to Dirichlet boundary conditions , where is a real Fourier multiplier. More precisely, they show that, for a typical Fourier multiplier , any solution with the initial datum in the -neighborhood of a KAM torus still stays in the -neighborhood of the KAM torus for a polynomial long time such as for any given with , where is a constant depending on and as .
Download or read book Proceedings of the International Congress of Mathematicians written by S.D. Chatterji and published by Birkhäuser. This book was released on 2012-12-06 with total page 1669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first ICM was held in Zürich in 1897, it has become the pinnacle of mathematical gatherings. It aims at giving an overview of the current state of different branches of mathematics and its applications as well as an insight into the treatment of special problems of exceptional importance. The proceedings of the ICMs have provided a rich chronology of mathematical development in all its branches and a unique documentation of contemporary research. They form an indispensable part of every mathematical library. The Proceedings of the International Congress of Mathematicians 1994, held in Zürich from August 3rd to 11th, 1994, are published in two volumes. Volume I contains an account of the organization of the Congress, the list of ordinary members, the reports on the work of the Fields Medalists and the Nevanlinna Prize Winner, the plenary one-hour addresses, and the invited addresses presented at Section Meetings 1 - 6. Volume II contains the invited address for Section Meetings 7 - 19. A complete author index is included in both volumes. '...the content of these impressive two volumes sheds a certain light on the present state of mathematical sciences and anybody doing research in mathematics should look carefully at these Proceedings. For young people beginning research, this is even more important, so these are a must for any serious mathematics library. The graphical presentation is, as always with Birkhäuser, excellent....' (Revue Roumaine de Mathematiques pures et Appliquées)
Download or read book Proceedings of the Workshop Nonlinear Physics Theory and Experiment II written by Mark J. Ablowitz and published by World Scientific. This book was released on 2003 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of solitons involves a broad variety of mathematical methods and appears in many areas of physics, technology, biology, and pure and applied mathematics. In this book, emphasis is placed on both theory (considering mathematical approaches for classical and quantum nonlinear systems ? both continuous and discrete) and experiment (with special discussions on high bit rate optical communications and pulse dynamics in optical materials).
Download or read book Nonlinear Physics Theory And Experiment Ii Proceedings Of The Workshop written by Barbara Prinari and published by World Scientific. This book was released on 2003-04-08 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of solitons involves a broad variety of mathematical methods and appears in many areas of physics, technology, biology, and pure and applied mathematics. In this book, emphasis is placed on both theory (considering mathematical approaches for classical and quantum nonlinear systems — both continuous and discrete) and experiment (with special discussions on high bit rate optical communications and pulse dynamics in optical materials).
Download or read book Global Solutions of Nonlinear Schr dinger Equations written by Jean Bourgain and published by American Mathematical Soc.. This book was released on 1999 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral and Scattering Theory written by M. Ikawa and published by CRC Press. This book was released on 2020-12-18 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This useful volume, based on the Taniguchi International Workshop held recently in Sanda, Hyogo, Japan, discusses current problems and offers the mostup-to-date methods for research in spectral and scattering theory."
Download or read book Kam Story The A Friendly Introduction To The Content History And Significance Of Classical Kolmogorov arnold moser Theory written by H Scott Dumas and published by World Scientific Publishing Company. This book was released on 2014-02-28 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science.The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a “breakthrough”). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory).Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.
