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Author : Jonathan Martin Jacobs
Publisher :
ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.:/5 (89 download)
Download or read book Unfoldings of Fixed Points of One-dimensional Dynamical Systems written by Jonathan Martin Jacobs and published by . This book was released on 1985 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Martin Golubitsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821850601
Total Pages : 408 pages
Book Rating : 4.8/5 (218 download)
Download or read book Multiparameter Bifurcation Theory written by Martin Golubitsky and published by American Mathematical Soc.. This book was released on 1986 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1985 AMS Summer Research Conference brought together mathematicians interested in multiparameter bifurcation with scientists working on fluid instabilities and chemical reactor dynamics. This proceedings volume demonstrates the mutually beneficial interactions between the mathematical analysis, based on genericity, and experimental studies in these fields. Various papers study steady state bifurcation, Hopf bifurcation to periodic solutions, interactions between modes, dynamic bifurcations, and the role of symmetries in such systems. A section of abstracts at the end of the volume provides guides and pointers to the literature. The mathematical study of multiparameter bifurcation leads to a number of theoretical and practical difficulties, many of which are discussed in these papers. The articles also describe theoretical and experimental studies of chemical reactors, which provide many situations in which to test the mathematical ideas. Other test areas are found in fluid dynamics, particularly in studying the routes to chaos in two laboratory systems, Taylor-Couette flow between rotating cylinders and Rayleigh-Benard convection in a fluid layer.
Author : Nessim Sibony
Publisher : Springer Science & Business Media
ISBN 13 : 3642131700
Total Pages : 357 pages
Book Rating : 4.6/5 (421 download)
Download or read book Holomorphic Dynamical Systems written by Nessim Sibony and published by Springer Science & Business Media. This book was released on 2010-07-31 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.
Author : Robert Gilmore
Publisher : John Wiley & Sons
ISBN 13 : 352763942X
Total Pages : 618 pages
Book Rating : 4.5/5 (276 download)
Download or read book The Topology of Chaos written by Robert Gilmore and published by John Wiley & Sons. This book was released on 2012-09-19 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deep understanding of the structure of strange attractors, how they are classified, and how the information required to identify and classify a strange attractor can be extracted from experimental data. In its first edition, the Topology of Chaos has been a valuable resource for physicist and mathematicians interested in the topological analysis of dynamical systems. Since its publication in 2002, important theoretical and experimental advances have put the topological analysis program on a firmer basis. This second edition includes relevant results and connects the material to other recent developments. Following significant improvements will be included: * A gentler introduction to the topological analysis of chaotic systems for the non expert which introduces the problems and questions that one commonly encounters when observing a chaotic dynamics and which are well addressed by a topological approach: existence of unstable periodic orbits, bifurcation sequences, multistability etc. * A new chapter is devoted to bounding tori which are essential for achieving generality as well as for understanding the influence of boundary conditions. * The new edition also reflects the progress which had been made towards extending topological analysis to higher-dimensional systems by proposing a new formalism where evolving triangulations replace braids. * There has also been much progress in the understanding of what is a good representation of a chaotic system, and therefore a new chapter is devoted to embeddings. * The chapter on topological analysis program will be expanded to cover traditional measures of chaos. This will help to connect those readers who are familiar with those measures and tests to the more sophisticated methodologies discussed in detail in this book. * The addition of the Appendix with both frequently asked and open questions with answers gathers the most essential points readers should keep in mind and guides to corresponding sections in the book. This will be of great help to those who want to selectively dive into the book and its treatments rather than reading it cover to cover. What makes this book special is its attempt to classify real physical systems (e.g. lasers) using topological techniques applied to real date (e.g. time series). Hence it has become the experimenter?s guidebook to reliable and sophisticated studies of experimental data for comparison with candidate relevant theoretical models, inevitable to physicists, mathematicians, and engineers studying low-dimensional chaotic systems.
Author : Santiago Ibáñez
Publisher : Springer Science & Business Media
ISBN 13 : 3642388302
Total Pages : 426 pages
Book Rating : 4.6/5 (423 download)
Download or read book Progress and Challenges in Dynamical Systems written by Santiago Ibáñez and published by Springer Science & Business Media. This book was released on 2013-09-20 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers based on talks given at the International Conference Dynamical Systems: 100 years after Poincaré held at the University of Oviedo, Gijón in Spain, September 2012. It provides an overview of the state of the art in the study of dynamical systems. This book covers a broad range of topics, focusing on discrete and continuous dynamical systems, bifurcation theory, celestial mechanics, delay difference and differential equations, Hamiltonian systems and also the classic challenges in planar vector fields. It also details recent advances and new trends in the field, including applications to a wide range of disciplines such as biology, chemistry, physics and economics. The memory of Henri Poincaré, who laid the foundations of the subject, inspired this exploration of dynamical systems. In honor of this remarkable mathematician, theoretical physicist, engineer and philosopher, the authors have made a special effort to place the reader at the frontiers of current knowledge in the discipline.
Author : James D. Meiss
Publisher : SIAM
ISBN 13 : 9780898718232
Total Pages : 409 pages
Book Rating : 4.7/5 (182 download)
Download or read book Differential Dynamical Systems written by James D. Meiss and published by SIAM. This book was released on 2007-01-01 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems conceptsflow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems. Audience This textbook is intended for senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with elementary differential equations and linear algebra and should have had exposure to advanced calculus. Contents List of Figures; Preface; Acknowledgments; Chapter 1: Introduction; Chapter 2: Linear Systems; Chapter 3: Existence and Uniqueness; Chapter 4: Dynamical Systems; Chapter 5: Invariant Manifolds; Chapter 6: The Phase Plane; Chapter 7: Chaotic Dynamics; Chapter 8: Bifurcation Theory; Chapter 9: Hamiltonian Dynamics; Appendix: Mathematical Software; Bibliography; Index
Author : Conference Board of the Mathematical Sciences
Publisher : CRC Press
ISBN 13 : 9780824715298
Total Pages : 260 pages
Book Rating : 4.7/5 (152 download)
Download or read book Classical Mechanics and Dynamical Systems written by Conference Board of the Mathematical Sciences and published by CRC Press. This book was released on 1981-09-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
ISBN 13 : 1475739788
Total Pages : 648 pages
Book Rating : 4.4/5 (757 download)
Download or read book Elements of Applied Bifurcation Theory written by Yuri Kuznetsov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
Author : M. M. Peixoto
Publisher : Academic Press
ISBN 13 : 1483269108
Total Pages : 764 pages
Book Rating : 4.4/5 (832 download)
Download or read book Dynamical Systems written by M. M. Peixoto and published by Academic Press. This book was released on 2014-05-10 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical Systems is a collection of papers that deals with the generic theory of dynamical systems, in which structural stability becomes associated with a generic property. Some papers describe structural stability in terms of mappings of one manifold into another, as well as their singularities. One paper examines the theory of polyhedral catastrophes, particularly, the analogues of each of the four basic differentiable catastrophes which map the line. Other papers discuss isolating blocks, the exponential rate conditions for dynamical systems, bifurcation, catastrophe, and a nondensity theorem. One paper reviews the results of functional differential equations which show that a qualitative theory will emerge despite the presence of an infinite dimensionality or of a semigroup property. Another paper discusses a class of quasi-periodic solutions for Hamiltonian systems of differential equations. These equations generalize a well-known result of Kolmogorov and Arnold on perturbations of n-dimensional invariant tori for Hamiltonian systems of n degrees of freedom. The researcher can derive mathematical models based on qualitative mathematical argument by using as "axioms" three dynamic qualities found in heart muscle fibers and nerve axons. The collection can prove useful for mathematicians, students and professors of advanced mathematics, topology or calculus.
Author : Tönu Puu
Publisher : Springer Science & Business Media
ISBN 13 : 3540246991
Total Pages : 556 pages
Book Rating : 4.5/5 (42 download)
Download or read book Attractors, Bifurcations, & Chaos written by Tönu Puu and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.
Author : Philip Holmes
Publisher : Cambridge University Press
ISBN 13 : 1107008255
Total Pages : 403 pages
Book Rating : 4.1/5 (7 download)
Download or read book Turbulence, Coherent Structures, Dynamical Systems and Symmetry written by Philip Holmes and published by Cambridge University Press. This book was released on 2012-02-23 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.
Author : Bernold Fiedler
Publisher : Springer Science & Business Media
ISBN 13 : 3642565891
Total Pages : 816 pages
Book Rating : 4.6/5 (425 download)
Download or read book Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems written by Bernold Fiedler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.
Author : H. Broer
Publisher : Elsevier
ISBN 13 : 0080932266
Total Pages : 556 pages
Book Rating : 4.0/5 (89 download)
Download or read book Handbook of Dynamical Systems written by H. Broer and published by Elsevier. This book was released on 2010-11-10 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. - Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems - Highlights developments that are the foundation for future research in this field - Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems
Author : Stephen Wiggins
Publisher : Springer Science & Business Media
ISBN 13 : 1475740670
Total Pages : 685 pages
Book Rating : 4.4/5 (757 download)
Download or read book Introduction to Applied Nonlinear Dynamical Systems and Chaos written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an introduction to applied nonlinear dynamics and chaos. The emphasis is on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains an extensive bibliography and a detailed glossary of terms.
Author : Ardshir Guran
Publisher : World Scientific
ISBN 13 : 9789810229825
Total Pages : 254 pages
Book Rating : 4.2/5 (298 download)
Download or read book Nonlinear Dynamics written by Ardshir Guran and published by World Scientific. This book was released on 1997 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers on the subject of nonlinear dynamics and its applications written by experts in this field. It offers the reader a sampling of exciting research areas in this fast-growing field. The topics covered include chaos, tools to analyze motions, fractal boundaries, dynamics of the Fitzhugh-Nagumo equation, structural control, separation of contaminations from signal of interest, parametric excitation, stochastic bifurcation, mode localization in repetitive structures, Toda lattice, transition from soliton to chaotic motion, nonlinear normal modes, noise perturbations of nonlinear dynamical systems, and phase locking of coupled limit cycle oscillators. Mathematical methods include Lie transforms, Monte Carlo simulations, stochastic calculus, perturbation methods and proper orthogonal decomposition. Applications include gyrodynamics, tether connected satellites, shell buckling, nonlinear circuits, volume oscillations of a large lake, systems with stick-slip friction, imperfect or disordered structures, overturning of rigid blocks, central pattern generators, flow induced oscillations, shape control and vibration suppression of elastic structures.All of these diverse contributions have a common thread: the world of nonlinear behavior. Although linear dynamics is an invaluable tool, there are many problems where nonlinear effects are essential. Some examples include bifurcation of solutions, stability of motion, the effects of large displacements, and subharmonic resonance. This book shows how nonlinear dynamics is currently being utilized and investigated. It will be of interest to engineers, applied mathematicians and physicists.
Author : O. Regev
Publisher : Cambridge University Press
ISBN 13 : 9780521855341
Total Pages : 492 pages
Book Rating : 4.8/5 (553 download)
Download or read book Chaos and Complexity in Astrophysics written by O. Regev and published by Cambridge University Press. This book was released on 2006-03-23 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: A primer for researchers and graduate students; introduces and applies chaos techniques to specific astrophysical systems.
Author : Mario Bernardo
Publisher : Springer Science & Business Media
ISBN 13 : 1846287081
Total Pages : 497 pages
Book Rating : 4.8/5 (462 download)
Download or read book Piecewise-smooth Dynamical Systems written by Mario Bernardo and published by Springer Science & Business Media. This book was released on 2008-01-01 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.
