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 ...
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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.
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Add this copy of Lectures on Closed Geodesics to cart. $89.91, new condition, Sold by Educational Media Centre rated 4.0 out of 5 stars, ships from New Delhi, DELHI, INDIA, published 2011 by Springer.
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First edition, first printing, 227 pp., hardcover, fine. -If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
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Good. Springer-Verlag, 1978. Cover very lightly rubbed/bumped/soiled, faintly sunned, spine lightly sunned, top corners/spine ends lightly rubbed/bumped; edges very lightly rubbed/bumped/soiled, faintly sunned; interior very faintly age-toned throughout, rear endpaper very lightly soiled near the bottom corner, inscription by previous owner/marking in indelible ink at the top edge of the front pastedown; binding tight; cover, edges and interior intact and clean, except where noted. hardcover. Good.
Add this copy of Lectures on Closed Geodesics to cart. $83.83, new condition, Sold by Educational Media Centre rated 4.0 out of 5 stars, ships from New Delhi, DELHI, INDIA, published 1978 by Springer.
