By Bhimsen K. Shivamoggi
This e-book begins with a dialogue of nonlinear usual differential equations, bifurcation conception and Hamiltonian dynamics. It then embarks on a scientific dialogue of the conventional subject matters of contemporary nonlinear dynamics -- integrable structures, Poincaré maps, chaos, fractals and unusual attractors. The Baker’s transformation, the logistic map and Lorenz approach are mentioned intimately in view in their critical position within the topic. there's a designated dialogue of solitons situated round the Korteweg-deVries equation in view of its significant position in integrable structures. Then, there's a dialogue of the Painlevé estate of nonlinear differential equations which turns out to supply a try out of integrability. ultimately, there's a designated dialogue of the appliance of fractals and multi-fractals to fully-developed turbulence -- an issue whose realizing has been significantly enriched through the appliance of the ideas and techniques of contemporary nonlinear dynamics. at the software facet, there's a distinct emphasis on a few facets of fluid dynamics and plasma physics reflecting the author’s involvement in those components of physics. a couple of routines were only if diversity from uncomplicated functions to occasional huge extension of the speculation. ultimately, the record of references given on the finish of the publication includes essentially books and papers utilized in constructing the lecture fabric this quantity is predicated on.
This publication has grown out of the author’s lecture notes for an interdisciplinary graduate-level path on nonlinear dynamics. the elemental options, language and result of nonlinear dynamical structures are defined in a transparent and coherent approach. so as to let for an interdisciplinary readership, a casual kind has been followed and the mathematical formalism has been saved 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 vulnerable 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 recent fabric like thought of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and demanding phenomena views at the fluid turbulence challenge and lots of new exercises.