Overview

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. The author's intuitive approach forms a treatment that is comprehensible to relative beginners, yet rigorous enough for professional mathematicians. Integration on manifolds plays an important role in the text and provides the foundation for many concrete applications. Special attention is given to chaotic phenomena, including the persistence of chaos under small perturbations. The author also provides a unique presentation of the Conley index theory, which then forms the basis of an original approach to hyperbolic dynamics.

Full Product Details

Author:   Keith Burns (Northwestern University, Evanston, Illinois, USA) ,  Marian Gidea (Northeastern Illinois University, Chicago, USA) ,  Marian Gidea (Northeastern Illinois University, Chicago, USA)
Publisher:   Taylor & Francis Inc
Imprint:   Chapman & Hall/CRC
Dimensions:   Width: 15.60cm , Height: 2.80cm , Length: 23.40cm
Weight:   0.900kg
ISBN:  

9781584882534

ISBN 10:   1584882530
Pages:   400
Publication Date:   27 May 2005
Audience:   General/trade ,  College/higher education ,  General ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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

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

Author Information

Keith Burns, Marian Gidea

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