Geodesic Flows (Progress in Mathematics) [Hardcover]

Gabriel P. Paternain (Author)

Book Description

ISBN-10: 0817641440 | ISBN-13: 978-0817641443 | Publication Date: September 1, 1999 | Edition: 1

This work begins with an introduction to the geodesic flow of a complete Riemannian manifold, emphasizing its sympletic properties and culminating with various applications such as the non-existence of continuous invariant Lagrangian sub-bundles for manifolds with conjugate points. Subsequent chapters develop the relationship between the exponential growth rate of the average number of geodesic arcs between two points.

Editorial Reviews

Review

"The main goal of the book is to present, in a self-contained way, results of the author and of Ricardo Mane about various ways to calculate or estimate the topological entropy of the geodesic flow on a closed Riemannian manifold M. The book begins with two introductory chapters on general properties of geodesic flows including a discussion of some of its properties as a Hamiltonian system acting on the tangent bundle TM of M. The third and fourth chapters present a formula for the topological entropy of the geodesic flow in terms of asymptotic growth of the average number of geodesic arcs in M connecting two given points. This, and similar other formulas for the topological entropy are obtained as an application of a fundamental result of Y. Yomdin which is also discussed, however without proof. The last chapter contains results, mainly due to the author, on topological conditions for M which guarantee that the topological entropy of the geodesic flow for every metric on M is positive. It is also shown that there are manifolds which satisfy these conditions, but for which the infimum of the entropies for metrics with normalized volume vanishes. The text is accompanied by many exercises. Many of the easier details of the material are presented in this form…" –Zentralblatt Math "Unique and valuable... the presentation is clean and brisk...useful for self-study, and as a guide to the subject and its literature." –Mathematical Reviews

Product Details

• Hardcover: 162 pages
• Publisher: Birkhäuser Boston; 1 edition (September 1, 1999)
• Language: English
• ISBN-10: 0817641440
• ISBN-13: 978-0817641443
• Product Dimensions: 9.5 x 6.4 x 0.6 inches
• Shipping Weight: 14.4 ounces (View shipping rates and policies)
• Amazon Best Sellers Rank: #1,783,143 in Books (See Top 100 in Books)

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