Nonlinear dynamics and chaotic phenomena : an introduction

by Bhimsen K. Shivamoggi

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, Poincare 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 Painleve 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. GBP/LISTGBP

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[目次]

  • 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 Painleve Property of Dynamical Systems. Exercises. References. Index.

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この本の情報

書名 Nonlinear dynamics and chaotic phenomena : an introduction
著作者等 Shivamoggi, Bhimsen K.
シリーズ名 Fluid mechanics and its applications
出版元 Kluwer Academic
刊行年月 c1997
ページ数 xiii, 404 p.
大きさ 25 cm
ISBN 0792347722
NCID BA33404144
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言語 英語
出版国 オランダ
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