Download or read book Dynamical Systems VIII written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to applications of singularity theory in mathematics and physics, covering a broad spectrum of topics and problems. "The book contains a huge amount of information from all the branches of Singularity Theory, presented in a very attractive way, with lots of inspiring pictures." --ZENTRALBLATT MATH

Download or read book Dynamical Systems VIII written by V.I. Arnol'd and published by Springer. This book was released on 1993-04-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to applications of singularity theory in mathematics and physics, covering a broad spectrum of topics and problems. "The book contains a huge amount of information from all the branches of Singularity Theory, presented in a very attractive way, with lots of inspiring pictures." --ZENTRALBLATT MATH

Download or read book Dynamical Systems V written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.

Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

Download or read book Partial Differential Equations VIII written by M.A. Shubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the EMS contains three articles, on linear overdetermined systems of partial differential equations, dissipative Schroedinger operators, and index theorems. Each article presents a comprehensive survey of its subject, discussing fundamental results such as the construction of compatibility operators and complexes for elliptic, parabolic and hyperbolic coercive problems, the method of functional models and the Atiyah-Singer index theorem and its generalisations. Both classical and recent results are explained in detail and illustrated by means of examples.

Download or read book Dynamical Systems X written by Victor V. Kozlov and published by Springer Science & Business Media. This book was released on 2003-05-12 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. In addition, it details some interesting applications of the general theory of vortices, such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics.

Download or read book Asymptotic Behavior of Dynamical and Control Systems under Pertubation and Discretization written by Lars Grüne and published by Springer. This book was released on 2004-10-20 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors, asumptotically controllable sets and their respective domains of attractions and reachable sets. Combining robust stability concepts from nonlinear control theory, techniques from optimal control and differential games and methods from nonsmooth analysis, both qualitative and quantitative results are obtained and new algorithms are developed, analyzed and illustrated by examples.

Download or read book Asymptotic Behavior of Dynamical and Control Systems Under Perturbation and Discretization written by Lars Grüne and published by . This book was released on 2002 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an approach to the study of perturbation and discretization effects on the long-time behaviour of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors and asumptotically controllable sets.

Download or read book Differential Geometry Applied to Dynamical Systems written by Jean-Marc Ginoux and published by World Scientific. This book was released on 2009 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory OCo or the flow OCo may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes). In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.

Download or read book Dynamical Systems and Turbulence Warwick 1980 written by D. A. Rand and published by Springer. This book was released on 2006-11-14 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partial Differential Equations IX written by M.S. Agranovich and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This EMS volume gives an overview of the modern theory of elliptic boundary value problems, with contributions focusing on differential elliptic boundary problems and their spectral properties, elliptic pseudodifferential operators, and general differential elliptic boundary value problems in domains with singularities.

Download or read book Commutative Harmonic Analysis II written by Viktor Petrovich Khavin and published by Springer Science & Business Media. This book was released on 1998 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop, conquering new unexpected areas and producing impressive applications to a multitude of problems. It is widely understood that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This book is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in this volume can hardly be found.

Download or read book Dynamical Systems written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2005-11-24 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Breadth of scope is unique Author is a widely-known and successful textbook author Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples Includes a section on cellular automata

Download or read book General Topology III written by A. V. Arhangel' skii and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference work deals with important topics in general topology and their role in functional analysis and axiomatic set theory, for graduate students and researchers working in topology, functional analysis, set theory and probability theory. It provides a guide to recent research findings, with three contributions by Arhangel'skii and Choban.

Download or read book Algebraic Geometry II written by I.R. Shafarevich and published by Springer Science & Business Media. This book was released on 1995-12-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.

Download or read book Bifurcation and Stability in Nonlinear Dynamical Systems written by Albert C. J. Luo and published by Springer Nature. This book was released on 2020-01-30 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems. Until now, one does not have any efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums. For instance, infinite-equilibrium dynamical systems have higher-order singularity, which dramatically changes dynamical behaviors and possesses the similar characteristics of discontinuous dynamical systems. The stability and bifurcation of equilibriums on the specific eigenvector are presented, and the spiral stability and Hopf bifurcation of equilibriums in nonlinear systems are presented through the Fourier series transformation. The bifurcation and stability of higher-order singularity equilibriums are presented through the (2m)th and (2m+1)th -degree polynomial systems. From local analysis, dynamics of infinite-equilibrium systems is discussed. The research on infinite-equilibrium systems will bring us to the new era of dynamical systems and control. Presents an efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums; Discusses dynamics of infinite-equilibrium systems; Demonstrates higher-order singularity.

Download or read book Probability Theory III written by Yurij V. Prokhorov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the Encyclopaedia is a survey of stochastic calculus, an increasingly important part of probability, authored by well-known experts in the field. The book addresses graduate students and researchers in probability theory and mathematical statistics, as well as physicists and engineers who need to apply stochastic methods.