Nonlinear Dynamics and Chaotic Phenomena
Subtitle: An Introduction
By: by Bhimsen K. Shivamoggi
Series: Fluid Mechanics and Its Applications -- 42; Fluid Mechanics and Its Applications -- 42
Publisher: Springer Netherlands
Published: 1997
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 410
ISBN-13: 9789048149261; 9789401724425
Subjects: Mechanics; Nuclear physics; Physics; Vibration
Description: 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£
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