quartonews.it » Math and Science » Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics)

Author: | Marian Gidea,Keith Burns |

Subcategory: | Mathematics |

Language: | English |

Publisher: | Chapman and Hall/CRC; 1 edition (May 27, 2005) |

Pages: | 400 pages |

Category: | Math and Science |

Rating: | 4.4 |

Other formats: | lrf doc azw txt |

It teaches all the differential geometry and topology notions that somebody needs in the study of dynamical systems.

It teaches all the differential geometry and topology notions that somebody needs in the study of dynamical systems. It completely enhanced my knowledge on the subject and took me to a higher level of understanding. 16 people found this helpful. The book by Burns and Gidea is also be strongly recommended for those readers who wish to enhance their mathematical tools to make possible a deeper insight into these fascinating physical theories. 5 people found this helpful.

Differential Geometry and Topology book. Start by marking Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics) as Want to Read: Want to Read savin. ant to Read. Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics). by. Keith Burns, Marian Gidea.

Keith Burns, Marian Gidea. 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

Differential Geometry and Topology: With a View to Dynamical Systems. Keith Burns, Marian Gidea, 2005.

Differential Geometry and Topology: With a View to Dynamical Systems. Download (pdf, . 1 Mb) Donate Read. eBook Rental from £4. 0. Chapman and Hall/CRC Published May 27, 2005 Textbook - 400 Pages - 132 B/W Illustrations ISBN 9781584882534 - CAT C2530 Series: Studies in Advanced Mathematics. 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.

The differential topology aspect of the book centers on classical, transversality theory, Sard's . The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart

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. 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.

this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. CRC Press, 27 May 2005 - 400 sayfa.

Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics.

This book offers a nice introduction to major topics in differential geometry and differential topology and their applications in the theory of dynamical systems

This book offers a nice introduction to major topics in differential geometry and differential topology and their applications in the theory of dynamical systems. It starts with a chapter on manifolds (including the Sard theorem), followed by a discussion of vector fields, the Lie derivative and Lie brackets, and discrete and smooth dynamical systems. The following chapters treat Riemannian manifolds, affine and Levi-Civita connections, geodesics, curvatures, Jacobi fields and conjugate points and the geodesic flow.

Автор: Burns, Keith Название: Differential Geometry and Topology: With a View to. .

The last three chapters study bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.

Keith Burns and Marian Gidea. This book begins with the basic theory of differentiable manifolds and includes a discussion of Sard's theorem and transversality. Publisher: Chapman&Hall/CRC. The modern theory of dynamical systems depends heavily on differential geometry and topology as, illustrated, for example, in the extensive background section included in Abraham and Marsden's Foundations of Mechanics. On the other hand, dynamical systems have provided both motivation and a multitude of non-trivial applications of the powerful tools of differential geometry and topology.

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.

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