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.
Keith Burns, Marian Gidea
"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
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