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OverviewFull Product DetailsAuthor: W. KlingenbergPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of the original 1st ed. 1978 Volume: 230 Dimensions: Width: 15.50cm , Height: 1.30cm , Length: 23.50cm Weight: 0.382kg ISBN: 9783642618833ISBN 10: 3642618839 Pages: 230 Publication Date: 13 October 2011 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1. The Hilbert Manifold of Closed Curves.- 1.1 Hilbert Manifolds.- 1.2 The Manifold of Closed Curves.- 1.3 Riemannian Metric and Energy Integral of the Manifold of Closed Curves.- 1.4 The Condition (C) of Palais and Smale and its Consequences.- 2. The Morse-Lusternik-Schnirelmann Theory on the Manifold of Closed Curves.- 2.1 The Lusternik-Schnirelmann Theory on ?M.- 2.2 The Space of Unparameterized Closed Curves.- 2.3 Closed Geodesics on Spheres.- 2.4 Morse Theory on ?M.- 2.5 The Morse Complex.- 3. The Geodesic Flow.- 3.1 Hamiltonian Systems.- 3.2 The Index Theorem for Closed Geodesics.- 3.3 Properties of the Poincaré Map.- 3.3 Appendix. The Birkhoff-Lewis Fixed Point Theorem. By J. Moser.- 4. On the Existence of Many Closed Geodesics.- 4.1 Critical Points in ?M and the Theorem of Fet.- 4.2 The Theorem of Gromoll-Meyer.- 4.3 The Existence of Infinitely Many Closed Geodesics.- 4.3 Appendix. The Minimal Model for the Rational Homotopy Type of ?M. By J. Sacks.- 4.4 Some Generic Existence Theorems.- 5. Miscellaneous Results.- 5.1 The Theorem of the Three Closed Geodesics.- 5.2 Some Special Manifolds of Elliptic Type.- 5.3 Geodesics on Manifolds of Hyperbolic and Parabolic Type.- Appendix. The Theorem of Lusternik and Schnirelmann.- A.2 Closed Curves without Self-intersections on the 2-sphere.- A.3 The Theorem of Lusternik and Schnirelmann.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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