Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics)
| Author | : | |
| Rating | : | 4.33 (739 Votes) |
| Asin | : | 1584882530 |
| Format Type | : | paperback |
| Number of Pages | : | 400 Pages |
| Publish Date | : | 2013-11-19 |
| Language | : | English |
DESCRIPTION:
It also furnishes some of the tools necessary for a complete understanding of the Morse theory. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow.Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigoro
…The authors have succeeded in the integration of geometric theory, topological theory, and concrete applications to dynamical systems.-Mathematical Reviews, Andrew BuckiThe authors of this book treat a great many topics very concisely.-MAA Reviews, William J. Satzer, 2005A 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 . The authors introduce important concepts by means of intuitive discussions and suggestive examples and follow them with significant applications, especially those related to dynamics
A very good book A very clear and very entertaining book for a course on differential geometry and topology (with a view to dynamical systems).First let me remark that talking about content, the book is very good. Each of the 9 chapters of the book offers intuitive insight while developing the main text and it does so without lacking in rigor. The first 6 chapters (which deal with manifolds, vector fields and dynamical systems, Riemannian metrics, Riemannian connections and geodesics, curvature and tensors and differential forms) make up an introduction to dynamical systems and Morse theory (the subjec. Jerzy Filus said Excellent book. It was a great pleasure to read the book “Differential Geometry and Topology With a View to Dynamical Systems” by Keith Burns and Marian Gidea. The topic of manifolds and its development, typically considered as “very abstract and difficult”, becomes for the reader of this outstanding book tangible and familiar. This joyful aspect of the book was achieved by the authors by setting the advanced material of differential geometry and topology as if on a “mobile bridge” or a “crossroad” that associates a(n) (primarily) unfamiliar abstract par