By Keith Burns,Marian Gidea

obtainable, concise, and self-contained, this booklet bargains a very good advent to 3 comparable matters: differential geometry, differential topology, and dynamical platforms. issues of unique curiosity addressed within the ebook comprise Brouwer's fastened aspect theorem, Morse thought, and the geodesic flow.

Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential types, and integration on manifolds give you the beginning for lots of purposes in dynamical structures and mechanics. The authors additionally speak about the Gauss-Bonnet theorem and its implications in non-Euclidean geometry versions.

The differential topology point of the booklet facilities on classical, transversality concept, Sard's theorem, intersection thought, and fixed-point theorems. the development of the de Rham cohomology builds additional arguments for the powerful connection among the differential constitution and the topological constitution. It additionally furnishes a number of the instruments precious for a whole figuring out of the Morse idea. those discussions are via an creation to the speculation of hyperbolic platforms, with emphasis at the vital function of the geodesic circulate.

The integration of geometric concept, topological conception, and urban purposes to dynamical structures set this ebook aside. With fresh, transparent prose and potent examples, the authors' intuitive technique creates a remedy that's understandable to relative newbies, but rigorous sufficient for people with extra historical past and event within the field.

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