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Differential Geometry And Topology
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Differential Geometry And Topology - neues Buch

ISBN: 9781584882534

ID: 9551138

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. 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. Books, Science and Geography~~Mathematics~~Geometry, Differential Geometry And Topology~~Book~~9781584882534~~Marian Gidea, Keith Burns, , , , , , , , , ,

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Differential Geometry and Topology - Burns, Keith; Gidea, Marian
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Burns, Keith; Gidea, Marian:

Differential Geometry and Topology - neues Buch

ISBN: 9781584882534

ID: 1633677

MANIFOLDS Introduction Review of topological concepts Smooth manifolds Smooth maps Tangent vectors and the tangent bundle Tangent vectors as derivations The derivative of a smooth map Orientation Immersions, embeddings and submersions Regular and critical points and values Manifolds with boundary Sard's theorem Transversality Stability Exercises VECTOR FIELDS AND DYNAMICAL SYSTEMS Introduction Vector fields Smooth dynamical systems Lie derivative, Lie bracket Discrete dynamical systems Hyperbolic fixed points and periodic orbits Exercises RIEMANNIAN METRICS Introduction Riemannian metrics Standard geometries on surfaces Exercises RIEMANNIAN CONNECTIONS AND GEODESICS Introduction Affine connections Riemannian connections Geodesics The exponential map Minimizing properties of geodesics The Riemannian distance Exercises CURVATURE Introduction The curvature tensor The second fundamental form Sectional and Ricci curvatures Jacobi fields Manifolds of constant curvature Conjugate points Horizontal and vertical sub-bundles The geodesic flow Exercises TENSORS AND DIFFERENTIAL FORMS Introduction Vector bundles The tubular neighborhood theorem Tensor bundles Differential forms Integration of differential forms Stokes' theorem De Rham cohomology Singular homology The de Rham theorem Exercises FIXED POINTS AND INTERSECTION NUMBERS Introduction The Brouwer degree The oriented intersection number The fixed point index The Lefschetz number The Euler characteristic The Gauss-Bonnet theorem Exercises MORSE THEORY Introduction Nondegenerate critical points The gradient flow The topology of level sets Manifolds represented as CW complexes Morse inequalities Exercises HYPERBOLIC SYSTEMS Introduction Hyperbolic sets Hyperbolicity criteria Geodesic flows Exercises References Index Science Science eBook, CRC Press

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Differential Geometry and Topology: With a View to Dynamical Systems - Gidea, Marian / Burns, Keith Howard / Burns, Burns
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Differential Geometry and Topology: With a View to Dynamical Systems - gebrauchtes Buch

ISBN: 9781584882534

ID: 7178818

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: With a View to Dynamical Systems Gidea, Marian / Burns, Keith Howard / Burns, Burns, CRC Press

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Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics) - Gidea, Marian, Keith Howard Burns and Burns Burns
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23,6 x 16,0 x 2,8 cm, Gebundene Ausgabe 400 Seiten Gebundene Ausgabe Sofortversand! Gutes Exemplar, geringe Gebrauchsspuren, Cover/SU berieben/bestoßen, innen alles in Ordnung; good – fine Immediate delivery in bubble wrap envelope! Good copy, light signs of previous use, cover/dust jacket has some rubbing/wear (along the edges), interior in good condition 141110av23 ISBN: 9781584882534 gebraucht; gut, [PU:Chapman & Hall,]

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Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics) - Gidea, Marian, Keith Howard Burns and Burns Burns
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Gidea, Marian, Keith Howard Burns and Burns Burns:
Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics) - gebunden oder broschiert

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ID: 213326

400 Seiten 23,6 x 16,0 x 2,8 cm, Gebundene Ausgabe Sofortversand! Gutes Exemplar, geringe Gebrauchsspuren, Cover/SU berieben/bestoßen, innen alles in Ordnung; good – fine Immediate delivery in bubble wrap envelope! Good copy, light signs of previous use, cover/dust jacket has some rubbing/wear (along the edges), interior in good condition 141110av23 ISBN: 9781584882534 Versand D: 4,00 EUR, [PU:Chapman & Hall,]

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Details zum Buch
Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics)
Autor:

Gidea, Marian; Burns, Keith Howard; Burns, Burns

Titel:

Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics)

ISBN-Nummer:

9781584882534

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. The authors' intuitive approach forms a treatment that is comprehensible to relative beginners, yet rigorous enough for professional mathematicians. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, integration on manifolds, intersection theory provide the foundation for many applications in dynamical systems and mechanics. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow.

Detailangaben zum Buch - Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics)


EAN (ISBN-13): 9781584882534
ISBN (ISBN-10): 1584882530
Gebundene Ausgabe
Erscheinungsjahr: 2005
Herausgeber: CHAPMAN & HALL
320 Seiten
Gewicht: 0,694 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 22.05.2007 12:48:34
Buch zuletzt gefunden am 11.11.2016 14:11:38
ISBN/EAN: 9781584882534

ISBN - alternative Schreibweisen:
1-58488-253-0, 978-1-58488-253-4

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