Description - Differential Geometry and Topology by Keith Burns
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.
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