An Introduction to Dynamical Systems

Author: Kathleen Alligood,Tim Sauer,J.A. Yorke

Publisher: Springer

ISBN: 3642592813

Category: Mathematics

Page: 603

View: 8226

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.
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Author: Morris W. Hirsch,Stephen Smale,Robert L. Devaney

Publisher: Academic Press

ISBN: 0123497035

Category: Mathematics

Page: 417

View: 8483

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.
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Author: Robert Devaney

Publisher: CRC Press

ISBN: 0429981937

Category: Science

Page: 360

View: 1743

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.
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Eine Einführung für Naturwissenschaftler und Ingenieure

Author: John H. Argyris,Gunter Faust,Maria Haase

Publisher: Springer-Verlag

ISBN: 3322904415

Category: Mathematics

Page: 790

View: 4416

Das Buch stellt die grundlegenden Konzepte der Chaos-Theorie und die mathematischen Hilfsmittel so elementar wie möglich dar.
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Author: Serge Tabachnikov

Publisher: Springer-Verlag

ISBN: 3642319254

Category: Mathematics

Page: 165

View: 1470

Wie bewegt sich ein Massenpunkt in einem Gebiet, an dessen Rand er elastisch zurückprallt? Welchen Weg nimmt ein Lichtstrahl in einem Gebiet mit ideal reflektierenden Rändern? Anhand dieser und ähnlicher Fragen stellt das vorliegende Buch Zusammenhänge zwischen Billard und Differentialgeometrie, klassischer Mechanik sowie geometrischer Optik her. Dabei beschäftigt sich das Buch unter anderem mit dem Variationsprinzip beim mathematischen Billard, der symplektischen Geometrie von Lichtstrahlen, der Existenz oder Nichtexistenz von Kaustiken, periodischen Billardtrajektorien und dem Mechanismus für Chaos bei der Billarddynamik. Ergänzend wartet dieses Buch mit einer beachtlichen Anzahl von Exkursen auf, die sich verwandten Themen widmen, darunter der Vierfarbensatz, die mathematisch-physikalische Beschreibung von Regenbögen, der poincaresche Wiederkehrsatz, Hilberts viertes Problem oder der Schließungssatz von Poncelet.​
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Die Schönheit der Mathematik

Author: Steven Strogatz

Publisher: Kein & Aber AG

ISBN: 3036992693

Category: Mathematics

Page: 352

View: 6595

Mathematik durchdringt den ganzen Kosmos. Das weiß jeder, doch nur die wenigsten verstehen die Zusammenhänge wirklich. Steven Strogatz nimmt uns bei der Hand und spaziert mit uns durch diese Welt der Weisheit, Klarheit und Eleganz. Als Reiseleiter geht er neue, erfrischende Wege, deutet auf Besonderheiten, schildert Hintergründe und erklärt die unsichtbaren Mechanismen. Wir erfahren unter anderem von dem Wunder des Zählens, der genialen Einfachheit der Algebra, dem ewigen Erbe Newtons, dem Tango mit Quadraten, der Zweisamkeit von Primzahlen und der Macht des Unendlichen. Mit all seiner Begeisterung, seinem Scharfblick und seinem leichtem Ton hat Steven Strogatz ein herrliches Buch für alle geschrieben, die ihr Verständnis von Mathematik auf eine neue Art vertiefen möchten.
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Author: Stephen Wiggins

Publisher: Springer Science & Business Media

ISBN: 1475740670

Category: Mathematics

Page: 672

View: 7018

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.
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An Introduction

Author: Sandro Wimberger

Publisher: Springer

ISBN: 331906343X

Category: Science

Page: 206

View: 4390

The 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.
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Introduction for Applied Scientists and Engineers

Author: Francis C. Moon

Publisher: John Wiley & Sons

ISBN: 3527617515

Category: Science

Page: 528

View: 576

A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.
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Author: Robert A. Meyers

Publisher: Springer Science & Business Media

ISBN: 1461418054

Category: Mathematics

Page: 1858

View: 2969

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
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A Behavioral Approach

Author: J.C. Willems,J.W. Polderman

Publisher: Springer Science & Business Media

ISBN: 1475729537

Category: Mathematics

Page: 424

View: 3385

Using the behavioural approach to mathematical modelling, this book views a system as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems that are represented by systems of linear constant coefficients. The first part analyses the structure of the set of trajectories generated by such dynamical systems, and derives the conditions for two systems of differential equations to be equivalent in the sense that they define the same behaviour. In addition the memory structure of the system is analysed through state space models. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. In the third part, control problems are considered, in particular stabilisation and pole placement questions. Suitable for advanced undergraduate or beginning graduate students in mathematics and engineering, this text contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits.
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Theory And Experiment

Author: Robert L. Devaney

Publisher: Westview Press

ISBN: 9780813345475

Category: Science

Page: 320

View: 6930

A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It is designed as a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton's method, symbolic dynamics, the Julia set, and the Mandelbrot set, and includes biographies of some of the leading researchers in the field of dynamical systems. Mathematical and computer experiments are integrated throughout the text to help illustrate the meaning of the theorems presented.Chaotic Dynamical Systems Software, Labs 1–6 is a supplementary laboratory software package, available separately, that allows a more intuitive understanding of the mathematics behind dynamical systems theory. Combined with A First Course in Chaotic Dynamical Systems, it leads to a rich understanding of this emerging field.
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Ein Drogenkartell erfolgreich führen

Author: Tom Wainwright

Publisher: Karl Blessing Verlag

ISBN: 3641161746

Category: Business & Economics

Page: 352

View: 1725

Was haben Coca-Cola, McDonald’s und der internationale Drogenhandel gemeinsam? Der Drogenhandel ist ein globalisiertes, vernetztes und hoch professionalisiertes Geschäftsfeld mit einem Jahresumsatz von 300 Milliarden Dollar, Tendenz steigend. Wie man sich als aufstrebendes Kartell ein Stück vom Kuchen sichert? Indem man von den Besten des Big Business lernt. Denn die Strategien, die für Konzerne wie H&M, Coca-Cola und McDonald’s funktionieren, haben sich längst auch international erfolgreiche Drogenbarone angeeignet – von der richtigen PR über Offshoring, Assessment-Center und E-Commerce. In Narconomics vollzieht Wirtschaftsjournalist Wainwright die Wertschöpfungskette von Drogen wie Kokain nach, von der Koka-Ernte in den Anden bis zum Verkauf an unseren Straßenecken. Jahrelange Recherchen, gefahrenreiche Reisen zu den Brennpunkten des Drogenhandels und Interviews mit Beteiligten, ob minderjähriger Profikiller in den Straßen von Mexico City oder Polizist, Ganglord oder Staatspräsident, haben Wainwright tiefe Einblicke in eine einzigartig einträgliche und tödliche Branche beschert.
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Author: Ranjit Kumar Upadhyay,Satteluri R. K. Iyengar

Publisher: CRC Press

ISBN: 1439898863

Category: Mathematics

Page: 363

View: 9462

Introduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical models in natural systems, particularly ecological systems. Most of the models presented are solved using MATLAB®. The book first covers the necessary mathematical preliminaries, including testing of stability. It then describes the modeling of systems from natural science, focusing on one- and two-dimensional continuous and discrete time models. Moving on to chaotic dynamics, the authors discuss ways to study chaos, types of chaos, and methods for detecting chaos. They also explore chaotic dynamics in single and multiple species systems. The text concludes with a brief discussion on models of mechanical systems and electronic circuits. Suitable for advanced undergraduate and graduate students, this book provides a practical understanding of how the models are used in current natural science and engineering applications. Along with a variety of exercises and solved examples, the text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.
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An Introduction for Scientists and Engineers

Author: Robert C. Hilborn,Amanda and Lisa Cross Professor of Physics Robert Hilborn

Publisher: Oxford University Press on Demand

ISBN: 9780198507239

Category: Mathematics

Page: 650

View: 2350

This is a comprehensive introduction to the exciting scientific field of nonlinear dynamics for students, scientists, and engineers, and requires only minimal prerequisites in physics and mathematics. The book treats all the important areas in the field and provides an extensive and up-to-date bibliography of applications in all fields of science, social science, economics, and even the arts.
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Author: David Harvey

Publisher: Ullstein eBooks

ISBN: 3843710716

Category: Social Science

Page: 384

View: 9220

WORUM GEHT ES? Gibt es seit dem Ende des Kommunismus wirklich keine echten Alternativen zum Kapitalismus? David Harvey meint: Doch! Man muss allerdings das Wesen des Kapitalismus genau verstehen, um ihn durch einen revolutionären Humanismus ersetzen zu können, in dessen Zentrum nicht das Kapital, sondern der Mensch steht. Konkret untersucht Harvey die Anhäufung von Kapital, das fatale Wachstumscredo, den spekulativen Immobilienmarkt und den Raubbau an der Natur. Er beschreibt jedoch nicht nur Krisen, sondern zeigt auch Chancen auf. Denn gerade die Widersprüche im Kapitalismus können Anfangspunkte für neue politische und kulturelle Bewegungen sein. Die utopische Kraft dafür kommt aus den Städten. WAS IST BESONDERS? Eine fundierte, realitätsnahe Kapitalismuskritik und zugleich ein Manifest des Wandels – geschrieben von einem der führenden Sozialtheoretiker der heutigen Zeit. WER LIEST? • Jeder, der die globalen Machtverhältnisse kritisch sieht • Leser von Stéphane Hessel, Michael J. Sandel, David Graeber und Thomas Piketty
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An Introduction to Dynamical Systems

Author: Dominic William Jordan,Peter Smith

Publisher: Oxford University Press, USA

ISBN: 9780198565628

Category: Mathematics

Page: 550

View: 2072

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.
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An Elementary Introduction

Author: David P. Feldman

Publisher: Oxford University Press

ISBN: 0199566445

Category: Mathematics

Page: 408

View: 9808

For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.
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A Visual Introduction in 2 Dimensions

Author: Ralph Abraham,Laura Gardini,Christian Mira

Publisher: Springer Science & Business Media

ISBN: 1461219361

Category: Mathematics

Page: 246

View: 7082

The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.
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