ISBN: 9781584882534

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topic… More...

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer''s fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard''s theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors'' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field. | Differential Geometry and Topology by Keith Burns Hardcover | Indigo Chapters Books > Science & Nature > Math & Physics > Mathematics P10117, Keith Burns<

ISBN: 9781584882534

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. T… More...

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow.Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field. New Textbooks>Hardcover>Science>Mathematics>Mathematics, Taylor & Francis Core >2 >T<

2005, ISBN: 1584882530

[EAN: 9781584882534], Neubuch, [PU: Taylor & Francis Inc], MATHEMATICS GEOMETRY GENERAL, Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. O… More...

[EAN: 9781584882534], Neubuch, [PU: Taylor & Francis Inc], MATHEMATICS GEOMETRY GENERAL, Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 th., Books<

2005, ISBN: 9781584882534

Hardcover

Routledge, Hardcover, Auflage: 1, 400 Seiten, Publiziert: 2005-05-27T00:00:01Z, Produktgruppe: Book, 0.9 kg, Verkaufsrang: 2652393, Applied, Mathematics, Science & Math, Subjects, Books, … More...

Routledge, Hardcover, Auflage: 1, 400 Seiten, Publiziert: 2005-05-27T00:00:01Z, Produktgruppe: Book, 0.9 kg, Verkaufsrang: 2652393, Applied, Mathematics, Science & Math, Subjects, Books, Differential Geometry, Geometry & Topology, Number Theory, Pure Mathematics, Mathematical Physics, Science & Mathematics, New, Used & Rental Textbooks, Specialty Boutique, Routledge, 2005<