♥ Book Title : Operator Structures and Dynamical Systems
☯ Full Synopsis : "This volume contains the proceedings of a Leiden Workshop on Dynamical Systems and their accompanying Operator Structures which took place at the Lorentz Center in Leiden, The Netherlands, on July 21-25, 2008. These papers offer a panorama of selfadjoint and non-selfadjoint operator algebras associated with both noncommutative and commutative (topological) dynamical systems and related subjects. Papers on general theory, as well as more specialized ones on symbolic dynamics and complex dynamical systems, are included."Article| Marcel de Jeu| Statement ..."
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♥ Book Title : Entropy in Dynamical Systems
☯ Full Synopsis : "This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon–McMillan–Breiman Theorem, the Ornstein–Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research."Article| Tomasz Downarowicz| Statement ..."
♥ Book Title : Stochastic and spatial structures of dynamical systems
☯ Full Synopsis : ""Article| Sebastian van Strien| Statement ..."
♥ Book Title : Generalized Functions, Operator Theory, and Dynamical Systems
☯ Full Synopsis : "Nobel prize winner Ilya Prigogine writes in his preface: "Irreversibility is a challenge to mathematics...[which] leads to generalized functions and to an extension of spectral analysis beyond the conventional Hilbert space theory." Meeting this challenge required new mathematical formulations-obstacles met and largely overcome thanks primarily to the contributors to this volume." This compilation of works grew out of material presented at the "Hyperfunctions, Operator Theory and Dynamical Systems" symposium at the International Solvay Institutes for Physics and Chemistry in 1997. The result is a coherently organized collective work that moves from general, widely applicable mathematical methods to ever more specialized physical applications. Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems. The interplay between mathematics and physics is now more necessary than ever-and more difficult than ever, given the increasing complexity of theories and methods. Here the topics include:"Article| I Antoniou| Statement ..."
♥ Book Title : Operator Algebras in Dynamical Systems
☯ Full Synopsis : "This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made a considerable contribution. This is an active area of research, and one of the most ambitious aims of the theory is to develop quantum statistical mechanics within the framework of the C*-theory. The presentation, which is based on lectures given in Newcastle upon Tyne and Copenhagen, concentrates on topics involving quantum statistical mechanics and differentiations on manifolds. One of the goals is to formulate the absence theorem of phase transitions in its most general form within the C* setting. For the first time, he globally constructs, within that setting, derivations for a fairly wide class of interacting models, and presents a new axiomatic treatment of the construction of time evolutions and KMS states."Article| Shōichirō Sakai| Statement ..."
♥ Book Title : Turbulence, Coherent Structures, Dynamical Systems and Symmetry
☯ Full Synopsis : "Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics."Article| Philip Holmes| Statement ..."
♥ Book Title : Nonlinear Dynamical Systems of Mathematical Physics
☯ Full Synopsis : "This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field - including some innovations by the authors themselves - that have not appeared in any other book. The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville?Arnold and Mischenko?Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham?Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained. This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems."Article| Denis L. Blackmore| Statement ..."
♥ Book Title : Structural Dynamic Systems Com
☯ Full Synopsis : "The availability of powerful computers along with highly effective computational techniques have allowed computer-aided design and engineering of structural dynamics systems to achieve a high level of capability and importance. This volume clearly reveals the great significance of these techniques and the essential role they will play in the future as further development occurs. This will be a significant and unique reference for students, research workers, practitioners, computer scientists and others for years to come."Article| Cornelius T. Leondes| Statement ..."
♥ Book Title : System, Structure and Control 2004
☯ Full Synopsis : ""Article| Sabine Mondie| Statement ..."
♥ Book Title : Lectures on Dynamical Systems, Structural Stability, and Their Applications
☯ Full Synopsis : "The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems."Article| Kotik K. Lee| Statement ..."
♥ Book Title : Adaptive Control of Nonsmooth Dynamic Systems
☯ Full Synopsis : "Many of the non-smooth, non-linear phenomena covered in this well-balanced book are of vital importance in almost any field of engineering. Contributors from all over the world ensure that no one area’s slant on the subjects predominates."Article| Gang Tao| Statement ..."
♥ Book Title : Random Dynamical Systems in Finance
☯ Full Synopsis : "The theory and applications of random dynamical systems (RDS) are at the cutting edge of research in mathematics and economics, particularly in modeling the long-run evolution of economic systems subject to exogenous random shocks. Despite this interest, there are no books available that solely focus on RDS in finance and economics. Exploring this emerging area, Random Dynamical Systems in Finance shows how to model RDS in financial applications. Through numerous examples, the book explains how the theory of RDS can describe the asymptotic and qualitative behavior of systems of random and stochastic differential/difference equations in terms of stability, invariant manifolds, and attractors. The authors present many models of RDS and develop techniques for implementing RDS as approximations to financial models and option pricing formulas. For example, they approximate geometric Markov renewal processes in ergodic, merged, double-averaged, diffusion, normal deviation, and Poisson cases and apply the obtained results to option pricing formulas. With references at the end of each chapter, this book provides a variety of RDS for approximating financial models, presents numerous option pricing formulas for these models, and studies the stability and optimal control of RDS. The book is useful for researchers, academics, and graduate students in RDS and mathematical finance as well as practitioners working in the financial industry."Article| Anatoliy Swishchuk| Statement ..."