Chaos: A Program Collection for the PC, Third Edition

this New Edition Strives Yet Again To Provide Readers With A Working Knowledge Of Chaos Theory And Dynamical Systems Through Parallel Introductory Explanations In The Book And Interaction With Carefully-selected Programs Supplied On The Accompanying Diskette. The Programs Enable Readers, Especially Advanced-undergraduate Students In Physics, Engineering, And Math, To Tackle Relevant Physical Systems Quickly On Their Pcs, Without Distraction From Algorithmic Details. For The Third Edition Of Chaos: A Program Collection For The Pc, Each Of The Previous Twelve Programs Is Polished And Rewritten In C++ (both Windows And Linux Versions Are Included). A New Program Treats Kicked Systems, An Important Class Of Two-dimensional Problems, Which Is Introduced In Chapter 13. Each Chapter Follows The Structure: Theoretical Background; Numerical Techniques; Interaction With The Program; Computer Experiments; Real Experiments And Empirical Evidence; Reference. Interacting With The Many Numerical Experiments Have Proven To Help Readers To Become Familiar With This Fascinating Topic And Even To Enjoy The Experience. Ithasbeenthirteenyearssincetheappearanceofthe?rsteditionofthisbook, and nine years after the second. Meanwhile, chaotic (or nonlinear) dynamics is established as an essential part of courses in physics and it still fascinates students, scientists and even nonacademic people, in particular because of the beauty of computer generated images appearing frequently in this?eld. Quite generally, computers are an ideal tool for exploring and demonstr- ing the intricate features of chaotic dynamics. The programs in the previous editions of this book have been designed to support such studies even for the non-experienced users of personal computers. However, caused by the rapid development of the computational world, these programs written in Turbo Pascal appeared in an old-fashioned design compared to the up-to-date st- dard.Evenmoreimportant,thoseprogramswouldnotproperlyoperateunder recent versions of the Windows operating system. In addition, there is an - creasing use of Linux operating systems. Therefore, for the present edition, all the programs have been entirely rewritten in C++ and, of course, revised and polished. Two version of the program codes are supplied working under Windows or Linux operating systems. We have again corrected a few passage in the text of the book and added somemorerecentdevelopmentsinthe?eldofchaoticdynamics.Finallyanew program treating the important class of two-dimensional discrete (‘kicked') systems has been added and described in Chap.13. "This new edition strives to provide teachers with a working knowledge of chaos theory and dynamical systems through parallel introductory explanations in the book and interaction with carefully-selected programs supplied on the accompanying CD-ROM. The programs enable readers, especially advanced-undergraduate students in physics, engineering, and math, to tackle relevant physical systems quickly on their PCs, without distraction from algorithmic details." "For the third edition of Chaos: A Program Collection for the PCs, each of the previous twelve programs is polished and rewritten in C++ (both Windows and Linux versions are included). A new program treats kicked systems, an important class of two dimensional problems, which is introduced in Chapter 13. Each chapter follows the structure: theoretical background; numerical techniques; interaction with the program; computer experiments; real experiments and empirical evidence; reference."--Jacket Cover......Page 1 Chaos, Third Edition......Page 3 ISBN 9783540748663......Page 4 Preface to the Third Edition......Page 6 Preface to the First Edition......Page 8 Contents......Page 12 1 Overview and Basic Concepts......Page 18 2 Nonlinear Dynamics and Deterministic Chaos......Page 28 3 Billiard Systems......Page 64 4 Gravitational Billiards: The Wedge......Page 86 5 The Double Pendulum......Page 108 6 Chaotic Scattering......Page 132 7 Fermi Acceleration......Page 154 8 The Duffing Oscillator......Page 174 9 Feigenbaum Scenario......Page 202 10 Nonlinear Electronic Circuits......Page 228 11 Mandelbrot and Julia Sets......Page 248 12 Ordinary Differential Equations......Page 272 13 Kicked Systems......Page 318 A System Requirements and Program Installation......Page 336 B General Remarks on Using the Programs......Page 340 Glossary......Page 344 Index......Page 352

This new edition strives yet again to provide readers with a working knowledge of chaos theory and dynamical systems. It does so through parallel introductory explanations in the book and interaction with carefully-selected programs supplied on the accompanying disk. The programs enable readers, especially advanced-undergraduate students in physics, engineering, and math, to tackle relevant physical systems quickly on their PCs, without distraction from algorithmic details. For the third edition of Chaos: A Program Collection for the PC, each of the previous twelve programs is polished and rewritten in C++ (both Windows and Linux versions are included). A new program treats kicked systems, an important class of two-dimensional problems.

Chaos: A Program Collection for the PC presents an outstanding selection of executable programs with introductory texts to chaos theory and its simulation. Students in physics, mathematics, and engineering will find a thorough introduction to fundamentals and applications in this field. Many numerical experiments and suggestions for further studies help the reader to become familiar with this fascinating topic. The second edition includes one CD-ROM, the executable programs are Windows 95 compatible. Unexpected and unpredictable behavior. In everyday life we feel safer and more comfortable with predictability and determinism: in technically controlled processes, small mechanical forces are expected to cause minor changes; the time-table of trains is hopefully reliable; the motion of the earth and moon around the sun are thought to be regular and stable. This package presents a selection of executable programs designed to supplement undergraduate study on chaos theory and its computer simulation. Many numerical experiments and suggestions for further study should help the reader to become familiar with the field.