By Bhimsen K. Shivamoggi
This publication starts off with a dialogue of nonlinear usual differential equations, bifurcation conception and Hamiltonian dynamics. It then embarks on a scientific dialogue of the conventional themes of contemporary nonlinear dynamics -- integrable structures, Poincaré maps, chaos, fractals and weird attractors. The Baker’s transformation, the logistic map and Lorenz method are mentioned intimately in view in their critical position within the topic. there's a distinctive dialogue of solitons based round the Korteweg-deVries equation in view of its important position in integrable structures. Then, there's a dialogue of the Painlevé estate of nonlinear differential equations which turns out to supply a attempt of integrability. eventually, there's a designated dialogue of the appliance of fractals and multi-fractals to fully-developed turbulence -- an issue whose figuring out has been significantly enriched via the applying of the innovations and techniques of recent nonlinear dynamics. at the software aspect, there's a unique emphasis on a few points of fluid dynamics and plasma physics reflecting the author’s involvement in those parts of physics. a number of workouts were only if diversity from uncomplicated purposes to occasional enormous extension of the idea. eventually, the record of references given on the finish of the publication includes essentially books and papers utilized in constructing the lecture fabric this quantity relies on.
This booklet has grown out of the author’s lecture notes for an interdisciplinary graduate-level direction on nonlinear dynamics. the fundamental ideas, language and result of nonlinear dynamical platforms are defined in a transparent and coherent means. with a view to permit for an interdisciplinary readership, an off-the-cuff kind has been followed and the mathematical formalism has been stored to a minimum.
This e-book is addressed to first-year graduate scholars in utilized arithmetic, physics, and engineering, and comes in handy additionally to any theoretically susceptible researcher within the actual sciences and engineering.
This moment variation constitutes an in depth rewrite of the textual content related to refinement and enhancement of the readability and precision, updating and amplification of numerous sections, addition of latest fabric like thought of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and important phenomena views at the fluid turbulence challenge and lots of new exercises.