Nonlinear Dynamics and Chaotic Phenomena

This book was developed from the author's lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. He describes 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 should be useful to any theoretically-inclined researcher in physical sciences and engineering.Among the 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.