Download or read book Dynamical Systems IX written by D.V. Anosov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "significant" subsets in the phase space. Hyperbolicity the property that under a small displacement of any of a trajectory consists in point of it to one side of the trajectory, the change with time of the relative positions of the original and displaced points resulting from the action of the DS is reminiscent of the mot ion next to a saddle. If there are "sufficiently many" such trajectories and the phase space is compact, then although they "tend to diverge from one another" as it were, they "have nowhere to go" and their behaviour acquires a complicated intricate character. (In the physical literature one often talks about "chaos" in such situations. ) This type of be haviour would appear to be the opposite of the more customary and simple type of behaviour characterized by its own kind of stability and regularity of the motions (these words are for the moment not being used as a strict ter 1 minology but rather as descriptive informal terms). The ergodic properties of DS's with hyperbolic behaviour of trajectories (Bunimovich et al. 1985) have already been considered in Volume 2 of this series. In this volume we therefore consider mainly the properties of a topological character (see below 2 for further details).
Download or read book Dynamical Systems IX written by D.V. Anosov and published by Springer. This book was released on 2012-11-30 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "significant" subsets in the phase space. Hyperbolicity the property that under a small displacement of any of a trajectory consists in point of it to one side of the trajectory, the change with time of the relative positions of the original and displaced points resulting from the action of the DS is reminiscent of the mot ion next to a saddle. If there are "sufficiently many" such trajectories and the phase space is compact, then although they "tend to diverge from one another" as it were, they "have nowhere to go" and their behaviour acquires a complicated intricate character. (In the physical literature one often talks about "chaos" in such situations. ) This type of be haviour would appear to be the opposite of the more customary and simple type of behaviour characterized by its own kind of stability and regularity of the motions (these words are for the moment not being used as a strict ter 1 minology but rather as descriptive informal terms). The ergodic properties of DS's with hyperbolic behaviour of trajectories (Bunimovich et al. 1985) have already been considered in Volume 2 of this series. In this volume we therefore consider mainly the properties of a topological character (see below 2 for further details).
Download or read book Dynamical Systems IX written by and published by . This book was released on 1995 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamical Systems X written by Victor V. Kozlov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 193 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 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 Applied Nonautonomous and Random Dynamical Systems written by Tomás Caraballo and published by Springer. This book was released on 2017-01-31 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the theory of non-autonomous and stochastic dynamical systems, with a focus on the importance of the theory in the Applied Sciences. It starts by discussing the basic concepts from the theory of autonomous dynamical systems, which are easier to understand and can be used as the motivation for the non-autonomous and stochastic situations. The book subsequently establishes a framework for non-autonomous dynamical systems, and in particular describes the various approaches currently available for analysing the long-term behaviour of non-autonomous problems. Here, the major focus is on the novel theory of pullback attractors, which is still under development. In turn, the third part represents the main body of the book, introducing the theory of random dynamical systems and random attractors and revealing how it may be a suitable candidate for handling realistic models with stochasticity. A discussion of future research directions serves to round out the coverage.
Download or read book Dynamical Systems written by George David Birkhoff and published by . This book was released on 1927 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamical Systems with Hyperbolic Behavior written by D. V. Anosov and published by Springer Verlag. This book was released on 1995 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stability of Dynamical Systems written by Xiaoxin Liao and published by Elsevier. This book was released on 2007-08-01 with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems. Presents comprehensive theory and methodology of stability analysis Can be used as textbook for graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, scientific computation Serves as a comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers
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 Dynamical Systems and Processes written by Michel Weber and published by European Mathematical Society. This book was released on 2009 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in a concise and accessible way, as well as in a common setting, various tools and methods arising from spectral theory, ergodic theory and stochastic processes theory, which form the basis of and contribute interactively a great deal to the current research on almost-everywhere convergence problems. Researchers working in dynamical systems and at the crossroads of spectral theory, ergodic theory and stochastic processes will find the tools, methods, and results presented in this book of great interest. It is written in a style accessible to graduate students.
Download or read book Dynamical Systems I written by D.V. Anosov and published by Springer. This book was released on 1994-06-01 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." Journal de Physique
Download or read book Dynamical System Synchronization written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2013-03-22 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical System Synchronization (DSS) meticulously presents for the first time the theory of dynamical systems synchronization based on the local singularity theory of discontinuous dynamical systems. The book details the sufficient and necessary conditions for dynamical systems synchronizations, through extensive mathematical expression. Techniques for engineering implementation of DSS are clearly presented compared with the existing techniques.
Download or read book The Dynamical Systems Approach to Cognition written by Wolfgang Tschacher and published by World Scientific. This book was released on 2003 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: The shared platform of the articles collected in this volume is usedto advocate a dynamical systems approach to cognition. It is arguedthat recent developments in cognitive science towards an account ofembodiment, together with the general approach of complexity theoryand dynamics, have a major impact on behavioral and cognitivescience.
Download or read book Dynamical Systems Approach To Cognition The Concepts And Empirical Paradigms Based On Self organization Embodiment And Coordination Dynamics written by Wolfgang Tschacher and published by World Scientific. This book was released on 2003-10-14 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: The shared platform of the articles collected in this volume is used to advocate a dynamical systems approach to cognition. It is argued that recent developments in cognitive science towards an account of embodiment, together with the general approach of complexity theory and dynamics, have a major impact on behavioral and cognitive science. The book points out that there are two domains that follow naturally from the stance of embodiment: first, coordination dynamics is an established empirical paradigm that is best able to aid the approach; second, the obvious goal-directedness of intelligent action (i.e., intentionality) is nicely addressed in the framework of the dynamical synergetic approach.
Download or read book Differentiable Dynamical Systems written by Lan Wen and published by American Mathematical Soc.. This book was released on 2016-07-20 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to [email protected] for more information.
Download or read book Dynamical Systems written by C.M. Place and published by Routledge. This book was released on 2017-11-22 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses the qualitative properties of dynamical systems including both differential equations and maps. The approach taken relies heavily on examples (supported by extensive exercises, hints to solutions and diagrams) to develop the material, including a treatment of chaotic behavior. The unprecedented popular interest shown in recent years in the chaotic behavior of discrete dynamic systems including such topics as chaos and fractals has had its impact on the undergraduate and graduate curriculum. However there has, until now, been no text which sets out this developing area of mathematics within the context of standard teaching of ordinary differential equations. Applications in physics, engineering, and geology are considered and introductions to fractal imaging and cellular automata are given.
