Wiggins Introduction to Applied Nonlinear Dynamical Systems and Chaos

Erscheinungsjahr 2013
ISBN: 978-1-4757-4067-7
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 2, 672 Seiten, eBook

Reihe: Texts in Applied Mathematics

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM) . The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface This textbook was developed from material presented in a year-long, grad uate-level course in nonlinear dynamics that I taught at Caltech over the past five years. It contains the basic techniques and results I believe to be necessary for graduate students to begin research in the field.

Zielgruppe

Graduate

Autoren/Hrsg.

Wiggins, Stephen

Inhaltsverzeichnis

0 Introduction.- 1 The Geometrical Point of View of Dynamical Systems: Background Material, Poincaré Maps, and Examples.- 2 Methods for Simplifying Dynamical Systems.- 3 Local Bifurcations.- 4 Some Aspects of Global Bifurcation and Chaos.