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catalog abstract ""Geodesic flows are of considerable current interest since they are, perhaps, the most remarkable class of conservative dynamical systems. They provide a unified arena in which one can explore numerous interplays among several fields, including smooth ergodic theory, symplectic and Riemannian geometry, and algebraic topology." "This self-contained monograph will be of interest to graduate students and researchers of dynamical systems and differential geometry. Numerous exercises and examples as well as a comprehensive index and bibliography make this work an excellent self-study resource or text for a one-semester course or seminar."--Jacket.".
catalog contributor b11394826.
catalog created "1999.".
catalog date "1999".
catalog date "1999.".
catalog dateCopyrighted "1999.".
catalog description ""Geodesic flows are of considerable current interest since they are, perhaps, the most remarkable class of conservative dynamical systems. They provide a unified arena in which one can explore numerous interplays among several fields, including smooth ergodic theory, symplectic and Riemannian geometry, and algebraic topology."".
catalog description ""This self-contained monograph will be of interest to graduate students and researchers of dynamical systems and differential geometry. Numerous exercises and examples as well as a comprehensive index and bibliography make this work an excellent self-study resource or text for a one-semester course or seminar."--Jacket.".
catalog description "1. Introduction to Geodesic Flows. 1.1. Geodesic flow of a complete Riemannian manifold. 1.2. Symplectic and contact manifolds. 1.3. The geometry of the tangent bundle. 1.4. The cotangent bundle T*M. 1.5. Jacobi fields and the differential of the geodesic flow. 1.6. The asymptotic cycle and the stable norm -- 2. The Geodesic Flow Acting on Lagrangian Subspaces. 2.1. Twist properties. 2.2. Riccati equations. 2.3. The Grassmannian bundle of Lagrangian subspaces. 2.4. The Maslov index. 2.5. The geodesic flow acting at the level of Lagrangian subspaces. 2.6. Continuous invariant Lagrangian subbundles in SM. 2.7. Birkhoff's second theorem for geodesic flows -- 3. Geodesic Arcs, Counting Functions and Topological Entropy. 3.1. The counting functions. 3.2. Entropies and Yomdin's theorem. 3.3. Geodesic arcs and topological entropy. 3.4. Manning's inequality. 3.5. A uniform version of Yomdin's theorem -- 4. Mane's Formula for Geodesic Flows and Convex Billiards.".
catalog description "Includes bibliographical references and index.".
catalog extent "xii, 149 p. ;".
catalog identifier "0817641440 (alk. paper)".
catalog identifier "3764341440 (alk. paper)".
catalog isPartOf "Progress in mathematics (Boston, Mass.) ; v. 180.".
catalog isPartOf "Progress in mathematics ; v. 180".
catalog issued "1999".
catalog issued "1999.".
catalog language "eng".
catalog publisher "Boston, Mass. : Birkhäuser,".
catalog subject "514/.74 21".
catalog subject "Geodesic flows.".
catalog subject "QA614.82 .P38 1999".
catalog tableOfContents "1. Introduction to Geodesic Flows. 1.1. Geodesic flow of a complete Riemannian manifold. 1.2. Symplectic and contact manifolds. 1.3. The geometry of the tangent bundle. 1.4. The cotangent bundle T*M. 1.5. Jacobi fields and the differential of the geodesic flow. 1.6. The asymptotic cycle and the stable norm -- 2. The Geodesic Flow Acting on Lagrangian Subspaces. 2.1. Twist properties. 2.2. Riccati equations. 2.3. The Grassmannian bundle of Lagrangian subspaces. 2.4. The Maslov index. 2.5. The geodesic flow acting at the level of Lagrangian subspaces. 2.6. Continuous invariant Lagrangian subbundles in SM. 2.7. Birkhoff's second theorem for geodesic flows -- 3. Geodesic Arcs, Counting Functions and Topological Entropy. 3.1. The counting functions. 3.2. Entropies and Yomdin's theorem. 3.3. Geodesic arcs and topological entropy. 3.4. Manning's inequality. 3.5. A uniform version of Yomdin's theorem -- 4. Mane's Formula for Geodesic Flows and Convex Billiards.".
catalog title "Geodesic flows / Gabriel P. Paternain.".
catalog type "text".