Differential Geometry and Topology: With a View to Dynamical Systems

by Keith Burns, Marian Gidea

Overview

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics

Product Details

ISBN-13:	9781040168530
Publisher:	CRC Press
Publication date:	05/27/2005
Series:	Studies in Advanced Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	400
File size:	8 MB

About the Author

Keith Burns, Marian Gidea

Table of Contents

Manifolds. Vector Fields and Dynamical Systems. Riemannian Metrics. Riemannian Connections and Geodesics. Curvature. Tensors and Differential Forms. Fixed Points and Intersection Numbers. Morse Theory. Hyperbolic Systems. References. Index.

Editorial Reviews

"The authors introduce important concepts by means of intuitive discussions and suggestive examples and follow them with significant applications, especially those related to dynamics. …The authors have succeeded in the integration of geometric theory, topological theory, and concrete applications to dynamical systems."
-Mathematical Reviews, Andrew Bucki

"The authors of this book treat a great many topics very concisely."
-MAA Reviews, William J. Satzer, 2005

"A noteworthy feature of the presentation is that dynamical systems, which are introduced in the second chapter, are used systematically to illustrate concepts and as a source of applications."
-CMS Notes, Vol. 38, No. 2, March, 2006

". . . very well written, in a very pedagogical manner and it covers a lot of material in a very clear way. I think this is an ideal introduction to differential geometry and topology for beginning graduate students or advanced undergraduate students in mathematics, but it will be, also, useful to physicist or other scientists with an interest in differential geometry and dynamical systems."

– Paul Blaga, in Babes- Bolyai Mathematica, June 2007, Vol. 52, No. 2

"Numerous illustrations and exercises round off the picture of an original and very readable textbook."

– M. Kunzinger, in Monatshefte fur Math, 2007, Vol. 152, No. 1

From the Publisher