A Modern Introduction to Dynamical Systems


Author: Richard Brown
Publisher: Oxford University Press
ISBN: 0198743289
Category: Mathematics
Page: 432
View: 4090

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This text is a high-level introduction to the modern theory of dynamical systems; an analysis-based, pure mathematics course textbook in the basic tools, techniques, theory and development of both the abstract and the practical notions of mathematical modelling, using both discrete and continuous concepts and examples comprising what may be called the modern theory of dynamics. Prerequisite knowledge is restricted to calculus, linear algebra and basic differential equations, and all higher-level analysis, geometry and algebra is introduced as needed within the text. Following this text from start to finish will provide the careful reader with the tools, vocabulary and conceptual foundation necessary to continue in further self-study and begin to explore current areas of active research in dynamical systems.

An Introduction to Dynamical Systems


Author: D. K. Arrowsmith,C. M. Place
Publisher: Cambridge University Press
ISBN: 9780521316507
Category: Mathematics
Page: 423
View: 1576

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In recent years there has been an explosion of research centred on the appearance of so-called 'chaotic behaviour'. This book provides a largely self contained introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit this sort of behaviour. The early part of this book is based on lectures given at the University of London and covers the background to dynamical systems, the fundamental properties of such systems, the local bifurcation theory of flows and diffeomorphisms, Anosov automorphism, the horseshoe diffeomorphism and the logistic map and area preserving planar maps . The authors then go on to consider current research in this field such as the perturbation of area-preserving maps of the plane and the cylinder. This book, which has a great number of worked examples and exercises, many with hints, and over 200 figures, will be a valuable first textbook to both senior undergraduates and postgraduate students in mathematics, physics, engineering, and other areas in which the notions of qualitative dynamics are employed.

Introduction to Discrete Dynamical Systems and Chaos


Author: Mario Martelli
Publisher: John Wiley & Sons
ISBN: 1118031121
Category: Mathematics
Page: 344
View: 9123

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A timely, accessible introduction to the mathematics ofchaos. The past three decades have seen dramatic developments in thetheory of dynamical systems, particularly regarding the explorationof chaotic behavior. Complex patterns of even simple processesarising in biology, chemistry, physics, engineering, economics, anda host of other disciplines have been investigated, explained, andutilized. Introduction to Discrete Dynamical Systems and Chaos makes theseexciting and important ideas accessible to students and scientistsby assuming, as a background, only the standard undergraduatetraining in calculus and linear algebra. Chaos is introduced at theoutset and is then incorporated as an integral part of the theoryof discrete dynamical systems in one or more dimensions. Both phasespace and parameter space analysis are developed with ampleexercises, more than 100 figures, and important practical examplessuch as the dynamics of atmospheric changes and neuralnetworks. An appendix provides readers with clear guidelines on how to useMathematica to explore discrete dynamical systems numerically.Selected programs can also be downloaded from a Wiley ftp site(address in preface). Another appendix lists possible projects thatcan be assigned for classroom investigation. Based on the author's1993 book, but boasting at least 60% new, revised, and updatedmaterial, the present Introduction to Discrete Dynamical Systemsand Chaos is a unique and extremely useful resource for allscientists interested in this active and intensely studiedfield. An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.

Chaos

An Introduction to Dynamical Systems
Author: Kathleen Alligood,Tim Sauer,J.A. Yorke
Publisher: Springer
ISBN: 3642592813
Category: Mathematics
Page: 603
View: 7125

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BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.

An Introduction to Dynamical Systems

Continuous and Discrete
Author: Rex Clark Robinson
Publisher: Prentice Hall
ISBN: N.A
Category: Mathematics
Page: 652
View: 6843

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Geometric approach to differential equations - Linear systems - The flow : solutions of nonlinear equations - Phase portraits with emphasis on fixed points - Phase portraits using energy and other test functions - Periodic orbits - Chaotic attractors - Iteration of functions as dynamics - Periodic points of one-dimensional maps - Itineraries for one-dimensional maps - Invariant sets for one-dimensional maps - Periodic points of higher dimensional maps - Invariant sets for higher dimensional maps - Fractals.

Differential Equations, Dynamical Systems, and an Introduction to Chaos


Author: Morris W. Hirsch,Stephen Smale,Robert L. Devaney
Publisher: Academic Press
ISBN: 0123497035
Category: Mathematics
Page: 417
View: 1369

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This text is about the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It is an update of one of Academic Press's most successful mathematics texts ever published, which has become the standard textbook for graduate courses in this area. The authors are tops in the field of advanced mathematics. Steve Smale is a Field's Medalist, which equates to being a Nobel prize winner in mathematics. Bob Devaney has authored several leading books in this subject area. Linear algebra prerequisites toned down from first edition Inclusion of analysis of examples of chaotic systems, including Lorenz, Rosssler, and Shilnikov systems Bifurcation theory included throughout.

Introduction to the Modern Theory of Dynamical Systems


Author: Anatole Katok,Boris Hasselblatt
Publisher: Cambridge University Press
ISBN: 9780521575577
Category: Mathematics
Page: 802
View: 8509

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This book provides a self-contained comprehensive exposition of the theory of dynamical systems. The book begins with a discussion of several elementary but crucial examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate and up.

Introduction to Dynamical Systems


Author: Michael Brin,Garrett Stuck
Publisher: Cambridge University Press
ISBN: 9781139433976
Category: Mathematics
Page: N.A
View: 9268

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This book provides a broad introduction to the subject of dynamical systems, suitable for a one- or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to such areas as number theory, data storage, and Internet search engines. This book grew out of lecture notes from the graduate dynamical systems course at the University of Maryland, College Park, and reflects not only the tastes of the authors, but also to some extent the collective opinion of the Dynamics Group at the University of Maryland, which includes experts in virtually every major area of dynamical systems.

An Introduction to Dynamical Systems and Chaos


Author: G.C. Layek
Publisher: Springer
ISBN: 8132225562
Category: Mathematics
Page: 622
View: 8835

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The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.

Introduction to Differential Equations with Dynamical Systems


Author: Stephen L. Campbell,Richard Haberman
Publisher: Princeton University Press
ISBN: 1400841321
Category: Mathematics
Page: 472
View: 6980

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Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.

An introduction to the theory of smooth dynamical systems


Author: W. Szlenk
Publisher: John Wiley & Sons Inc
ISBN: N.A
Category: Mathematics
Page: 369
View: 3049

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Discusses the theoretical aspects and results of smooth dynamical systems. Covers dynamical systems on manifolds of one or two dimensions, generic properties, stability theory, invariant measures for differentiable dynamical systems, and topological entrophy. Contains definitions and exercises for problem-solving practice.

Analytical Mechanics

With an Introduction to Dynamical Systems
Author: Josef S. Török
Publisher: John Wiley & Sons
ISBN: 9780471332077
Category: Science
Page: 359
View: 3405

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A stimulating, modern approach to analytical mechanics Analytical Mechanics with an Introduction to Dynamical Systems offers a much–needed, up–to–date treatment of analytical dynamics to meet the needs of today′s students and professionals. This outstanding resource offers clear and thorough coverage of mechanics and dynamical systems, with an approach that offers a balance between physical fundamentals and mathematical concepts. Exceptionally well written and abundantly illustrated, the book contains over 550 new problems–more than in any other book on the subject–along with user–friendly computational models using MATLAB. Featured topics include: ∗ An overview of fundamental dynamics, both two– and three–dimensional ∗ An examination of variational approaches, including Lagrangian theory ∗ A complete discussion of the dynamics of rotating bodies ∗ Coverage of the three–dimensional dynamics of rigid bodies ∗ A detailed treatment of Hamiltonian systems and stability theory Ideal for advanced undergraduate and graduate students in mechanical engineering, physics, or applied mathematics, this distinguished text is also an excellent self–study or reference text for the practicing engineer or scientist.

Nonlinear Ordinary Differential Equations

An Introduction to Dynamical Systems
Author: Dominic William Jordan,Peter Smith
Publisher: Oxford University Press, USA
ISBN: 9780198565628
Category: Mathematics
Page: 550
View: 8254

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The text of this edition has been revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos. It is directed towards practical applications of the theory with examples and problems.

Introduction to Applied Nonlinear Dynamical Systems and Chaos


Author: Stephen Wiggins
Publisher: Springer Science & Business Media
ISBN: 0387217495
Category: Mathematics
Page: 844
View: 7973

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This introduction to applied nonlinear dynamics and chaos places emphasis 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 a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik

An Introduction to Sequential Dynamical Systems


Author: Henning Mortveit,Christian Reidys
Publisher: Springer Science & Business Media
ISBN: 9780387498799
Category: Mathematics
Page: 248
View: 3894

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This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.

Infinite-Dimensional Dynamical Systems

An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors
Author: James C. Robinson
Publisher: Cambridge University Press
ISBN: 9780521632041
Category: Mathematics
Page: 461
View: 5972

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This book develops the theory of global attractors for a class of parabolic PDEs which includes reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated in detail. A lengthy chapter on Sobolev spaces provides the framework that allows a rigorous treatment of existence and uniqueness of solutions for both linear time-independent problems (Poisson's equation) and the nonlinear evolution equations which generate the infinite-dimensional dynamical systems of the title. Attention then switches to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space which determines the asymptotic dynamics. In particular, the concluding chapters investigate in what sense the dynamics restricted to the attractor are themselves 'finite-dimensional'. The book is intended as a didactic text for first year graduates, and assumes only a basic knowledge of Banach and Hilbert spaces, and a working understanding of the Lebesgue integral.

Introduction to Dynamic Systems

Theory, Models, and Applications
Author: David G. Luenberger
Publisher: Wiley
ISBN: N.A
Category: Science
Page: 464
View: 4828

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Integrates the traditional approach to differential equations with the modern systems and control theoretic approach to dynamic systems, emphasizing theoretical principles and classic models in a wide variety of areas. Provides a particularly comprehensive theoretical development that includes chapters on positive dynamic systems and optimal control theory. Contains numerous problems.

An Introduction To Chaotic Dynamical Systems


Author: Robert Devaney
Publisher: CRC Press
ISBN: 0429981937
Category: Science
Page: 360
View: 4254

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The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.