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Author: Karl-G. Grosse-Erdmann
Publisher: Springer Science & Business Media
Published: 2011-08-24
Total Pages: 388
ISBN-13: 9781447121695
DOWNLOAD EBOOKThis book introduces the dynamics of linear operators, and covers selected, largely independent topics from linear dynamics. The text is supplemented with more than 350 exercises and many illustrations, and a ‘Sources and Comments’ section in each chapter.
Author: Steven H. Strogatz
Publisher: CRC Press
Published: 2018-05-04
Total Pages: 532
ISBN-13: 0429961111
DOWNLOAD EBOOKThis textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Author: Morris W. Hirsch
Publisher: Academic Press
Published: 2004
Total Pages: 433
ISBN-13: 0123497035
DOWNLOAD EBOOKThirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.
Author: Sandro Wimberger
Publisher: Springer
Published: 2014-05-13
Total Pages: 215
ISBN-13: 331906343X
DOWNLOAD EBOOKThe field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.
Author: Richard Kautz
Publisher: Oxford University Press
Published: 2011
Total Pages: 384
ISBN-13: 0199594570
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Author: Linda Chamberlain
Publisher: Routledge
Published: 2016-01-28
Total Pages: 252
ISBN-13: 1317714768
DOWNLOAD EBOOKPsychology and the social sciences are in need of a new foundation, one that provides a better model for understanding complex behavior. Chaos theory and its newest permutation, complexity theory, offers an innovative, exciting and potentially revolutionary leap forward in the evolution of scientific thought. In Clinical Chaos, therapists and theoreticians from various areas in the social sciences will explore the relevance and implications for non-linear dynamics in observing, explaining, and understanding human behavior. At last, the scientific search can again encompass surprise, transformation, unpredictability, and pattern. This book is intended to introduce social scientists to chaos through paths that are already familiar. By linking chaos theory with existing psychological theories and established areas of clinical pursuit, Clinical Chaos emphasizes the relevance of this new science in providing a more flexible useful model for complexities of life.
Author: S. Neil Rasband
Publisher: Courier Dover Publications
Published: 2015-08-19
Total Pages: 244
ISBN-13: 0486795993
DOWNLOAD EBOOKIntroduction to the concepts, applications, theory, and technique of chaos. Suitable for advanced undergraduates and graduate students and researchers. Requires familiarity with differential equations and linear vector spaces. 1990 edition.
Author: John H. Argyris
Publisher: Springer
Published: 2015-04-24
Total Pages: 884
ISBN-13: 3662460424
DOWNLOAD EBOOKThis book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures. "This book will be of valuable help for my lectures" Hermann Haken, Stuttgart "This text-book should not be missing in any introductory lecture on non-linear systems and deterministic chaos" Wolfgang Kinzel, Würzburg “This well written book represents a comprehensive treatise on dynamical systems. It may serve as reference book for the whole field of nonlinear and chaotic systems and reports in a unique way on scientific developments of recent decades as well as important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky University Oldenburg, Germany
Author: Stephen Wiggins
Publisher: Springer Science & Business Media
Published: 2006-04-18
Total Pages: 860
ISBN-13: 0387217495
DOWNLOAD EBOOKThis 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
Author: Kathleen Alligood
Publisher: Springer
Published: 2012-12-06
Total Pages: 620
ISBN-13: 3642592813
DOWNLOAD EBOOKBACKGROUND 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.
