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Zusatztext "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 Informationen zum Autor Keith Burns, Marian Gidea Klappentext Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. The authors' intuitive approach forms a treatment that is comprehensible to relative beginners, yet rigorous enough for professional mathematicians. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, integration on manifolds, and intersection theory provide the foundation for many applications in dynamical systems and mechanics. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Zusammenfassung Offers an introduction to three related subjects: differential geometry, differential topology, and dynamical systems. This book addresses topics such as Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. It also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. Inhaltsverzeichnis 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....
