Nonlinear Dynamics and Chaotic Phenomena: An Introduction by B.K ShivamoggiNonlinear Dynamics and Chaotic Phenomena: An Introduction by B.K Shivamoggi

Nonlinear Dynamics and Chaotic Phenomena: An Introduction

byB.K Shivamoggi

Paperback | January 28, 2011

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This book has grown out of the author's lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. The author describes in a clear and coherent way the basic concepts, language and results of nonlinear dynamical systems. In order to allow for an interdisciplinary readership, an informal style has been adopted and the mathematical formalism kept to a minimum. The book starts with a discussion of nonlinear differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics - integrable systems, Poincaré maps, chaos, fractals and strange attractors. Baker's transformation, the logistic map and the Lorenz system are discussed in detail. Finally, there are systematic discussions of the application of fractals to turbulence in fluids, and the Painlevé property of nonlinear differential equations. Exercises are given at the end of each chapter. This book is accessible to first-year graduate students in applied mathematics, physics and engineering, and is useful to any theoretically inclined researcher in physical sciences and engineering. Among the unique features of this book are: a strong middle ground between elementary undergraduate texts on the one hand, and advanced level monographs on the other the presentation of some original developments a thorough discussion of the application of fractals to turbulence in fluids. £/LIST£
Title:Nonlinear Dynamics and Chaotic Phenomena: An IntroductionFormat:PaperbackDimensions:423 pages, 9.25 × 6.1 × 0.01 inPublished:January 28, 2011Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048149266

ISBN - 13:9789048149261

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Table of Contents

Introduction to Chaotic Behavior in Nonlinear Dynamics. 1. Nonlinear Differential Equations. 2. Bifurcation Theory. 3. Hamiltonian Dynamics. 4. Integrable Systems. 5. Chaos in Conservative Systems. 6. Chaos in Dissipative Systems. Appendices. 7. Fractals and Multi-Fractals in Turbulence. 8. Singularity Analysis and the Painlevé Property of Dynamical Systems. Exercises. References. Index.