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Book Cover
E-RESOURCE
Author Korsch, H. J., 1944-

Title Chaos : a program collection for the PC / H.J. Korsch, H.-J. Jodl, T. Hartmann.

Published Berlin ; New York : Springer, [2008]
ò008

Copies

Location Call No. Status
 UniM INTERNET resource    AVAILABLE
Edition Third rev. and enlarged edition.
Physical description 1 online resource (xv, 341 pages) : illustrations
1 online resource (1 computer optical disc (4 3/4 in.)
Bibliography Includes bibliographical references and index.
Contents 1. Overview and basic concepts -- 1.1. Introduction -- 1.2. The programs -- 1.3. Literature on chaotic dynamics -- 2. Nonlinear dynamics and deterministic chaos -- 2.1. Deterministic chaos -- 2.2. Hamiltonian systems -- 2.2.1. Integrable and ergodic systems -- t 2.2.2. Poincar⥠sections -- 2.2.3. The KAM theorem -- 2.2.4. Homoclinic points -- 2.3. Dissipative dynamical systems -- 2.3.1. Attractors -- 2.3.2. Routes to chaos -- 2.4. Special topics -- 2.4.1. The Poincar⥭Birkhoff theorem -- 2.4.2. Continued fractions -- 2.4.3. The Lyapunov exponent -- 2.4.4. Fixed points of one-dimensional maps -- 2.4.5. Fixed points of two-dimensional maps -- 2.4.6. Bifurcations -- References -- 3. Billiard systems -- 3.1. Deformations of a circle billiard -- 3.2. Numerical techniques -- 3.3. Interacting with the program -- 3.4. Computer experiments -- 3.4.1. From regularity to chaos -- 3.4.2. Zooming in -- 3.4.3. Sensitivity and determinism -- 3.4.4. Suggestions for additional experiments -- 3.5. Suggestions for further studies -- 3.6. Real experiments and empirical evidence -- References.
4. Gravitational billiards : the wedge -- 4.1. The Poincar⥠mapping -- 4.2. Interacting with the program -- 4.3. Computer experiments -- 4.3.1. Periodic motion and phase space organization -- 4.3.2. Bifurcation phenomena -- 4.3.3. 'Plane filling' wedge billiards -- 4.3.4. Suggestions for additional experiments -- 4.4. Suggestions for further studies -- 4.5. Real experiments and empirical evidence -- References -- 5. The double pendulum -- 5.1. Equations of motion -- 5.2. Numerical algorithms -- 5.3. Interacting with the program -- 5.4. Computer experiments -- 5.4.1. Different types of motion -- 5.4.2. Dynamics of the double pendulum -- 5.4.3. Destruction of invariant curves -- 5.4.4. Suggestions for additional experiments -- 5.5. Real experiments and empirical evidence -- References -- 6. Chaotic scattering -- 6.1. Scattering off three disks -- 6.2. Numerical techniques -- 6.3. Interacting with the program -- 6.4. Computer experiments -- 6.4.1. Scattering functions and two-disk collisions -- 6.4.2. Tree organization of three-disk collisions -- 6.4.3. Unstable periodic orbits -- 6.4.4. Fractal singularity structure -- 6.4.5. Suggestions for additional experiments -- 6.5. Suggestions for further studies -- 6.6. Real experiments and empirical evidence -- References.
7. Fermi acceleration -- 7.1. Fermi mappings -- 7.2. Interacting with the program -- 7.3. Computer experiments -- 7.3.1. Exploring phase space for different wall oscillations -- 7.3.2. KAM curves and stochastic acceleration -- 7.3.3. Fixed points and linear stability -- 7.3.4. Absolute barriers -- 7.3.5. Suggestions for additional experiments -- 7.4. Suggestions for further studies -- 7.5. Real experiments and empirical evidence -- References -- 8. The Duffing oscillator -- 8.1. The Duffing equation -- 8.2. Numerical techniques -- 8.3. Interacting with the program -- 8.4. Computer experiments -- 8.4.1. Chaotic and regular oscillations -- 8.4.2. The free Duffing oscillator -- 8.4.3. Anharmonic vibrations : resonances and bistability -- 8.4.5. Suggestions for additional experiments -- 8.5. Suggestions for further studies -- 8.6. Real experiments and empirical evidence -- References -- 9. Feigenbaum scenario -- 9.1. One-dimensional maps -- 9.2. Interacting with the program -- 9.3. Computer experiments -- 9.3.1. Period-doubling bifurcations -- 9.3.2. The chaotic regime -- 9.3.3. Lyapunov exponents -- 9.3.4. The tent map -- 9.3.5. Suggestions for additional experiments -- 9.4. Suggestions for further studies -- 9.5. Real experiments and empirical evidence -- References.
10. Nonlinear electronic circuits -- 10.1. A chaos generator -- 10.2. Numerical techniques -- 10.3. Interacting with the program -- 10.4. Computer experiments -- 10.4.1. Hopf bifurcation -- 10.4.2. Period-doubling -- 10.4.3. Return map -- 10.4.4. Suggestions for additional experiments -- 10.5. Real experiments and empirical evidence -- References -- 11. Mandelbrot and Julia sets -- 11.1. Two-dimensional iterated maps -- 11.2. Numerical methods -- 11.3. Interacting with the program -- 11.4. Computer experiments -- 11.4.1. Mandelbrot and Julia-sets -- 11.4.2. Zooming into the Mandelbrot set -- 11.4.3. General two-dimension quadratic mappings -- 11.4.4. Suggestions for additional experiments -- 11.5. Suggestions for further studies -- 11.6. Real experiments and empirical evidence -- References.
12. Ordinary differential equations -- 12.1. Numerical techniques -- 12.2. Interacting with the program -- 12.3. Computer experiments -- 12.3.1. The pendulum -- 12.3.2. A simple Hopf bifurcation -- 12.3.3. The Duffing oscillator revisited -- 12.3.4. Hill's equation -- 12.3.5. The Lorenz attractor -- 12.3.6. The R诳sler attractor -- 12.3.7. The H⥮on-Heiles system -- 12.3.8. Suggestions for additional experiments -- 12.4. Suggestions for further studies -- References -- 13. Kicked systems -- 13.1. Interacting with the program -- 13.2. Computer experiments -- 13.2.1. The standard mapping -- 13.2.2. The kicked quartic oscillator -- 13.2.3. The kicked quartic oscillator with damping -- 13.2.4. H⥮on map -- 13.2.5. Suggestions for additional experiments -- 13.3. Real experiments and empirical evidence -- References -- A. System requirements and program installation -- A.1. System requirements -- A.2. Installing the programs -- A.2.1. Windows operating system -- A.2.2. Linux operating system -- A.3. Programs -- A.4. Third party software -- B. General remarks on using the programs -- B.1. Interaction with the programs -- b.2. Input of mathematical expressions -- Glossary -- Index.
Summary A Program Collection for the PC presents an outstanding selection of executable programs with introductory texts on chaos theory and its simulation. Students in physics, mathematics, and engineering will find a thorough intoduction to fundamentals and applications in this field. Many numerical experiments and suggestions for further studies help the reader to become familiar with this fascinationg topic.
Notes Description based on print version record.
Other author Jodl, H.-J., 1943-
Hartmann, T. (Timo)
Subject Chaotic behavior in systems -- Experiments -- Data processing.
Chaotic behavior in systems -- Computer programs.
Digital computer simulation.
Chaotic behavior in systems -- Computer programs.
Chaotic behavior in systems -- Experiments -- Data processing.
Digital computer simulation.
Electronic books.
ISBN 9783662029916 (electronic bk.)
366202991X (electronic bk.)
9783540748663
3540748660
Standard Number 10.1007/978-3-662-02991-6