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Lectures on Closed Geodesics
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Bibliographic Detail
Publisher Springer Verlag
Publication date October 13, 2011
Pages 227
Binding Paperback
Edition Reprint
Book category Adult Non-Fiction
ISBN-13 9783642618833
ISBN-10 3642618839
Dimensions 0 by 6.10 by 9.25 in.
Original list price $179.00
Summaries and Reviews
Amazon.com description: Product Description: The question of existence of c10sed geodesics on a Riemannian manifold and the properties of the corresponding periodic orbits in the geodesic flow has been the object of intensive investigations since the beginning of global differential geo­ metry during the last century. The simplest case occurs for c10sed surfaces of negative curvature. Here, the fundamental group is very large and, as shown by Hadamard [Had] in 1898, every non-null homotopic c10sed curve can be deformed into a c10sed curve having minimallength in its free homotopy c1ass. This minimal curve is, up to the parameterization, uniquely determined and represents a c10sed geodesic. The question of existence of a c10sed geodesic on a simply connected c10sed surface is much more difficult. As pointed out by Poincare [po 1] in 1905, this problem has much in common with the problem ofthe existence of periodic orbits in the restricted three body problem. Poincare [l.c.] outlined a proof that on an analytic convex surface which does not differ too much from the standard sphere there always exists at least one c10sed geodesic of elliptic type, i. e., the corres­ ponding periodic orbit in the geodesic flow is infinitesimally stable.

Editions
Hardcover
Book cover for 9783540083931
 
from Springer Verlag (January 1, 1978)
9783540083931 | details & prices | List price $179.00
About: The question of existence of c10sed geodesics on a Riemannian manifold and the properties of the corresponding periodic orbits in the geodesic flow has been the object of intensive investigations since the beginning of global differential geo­ metry during the last century.
Paperback
Book cover for 9783642618833
 
The price comparison is for this edition
Reprint edition from Springer Verlag (October 13, 2011)
9783642618833 | details & prices | 227 pages | List price $179.00
About: The question of existence of c10sed geodesics on a Riemannian manifold and the properties of the corresponding periodic orbits in the geodesic flow has been the object of intensive investigations since the beginning of global differential geo­ metry during the last century.

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