000			02055 a2200265 4500
999			_c55523 _d55523
008			210924b ||||| |||| 00| 0 eng d
020			_a9781461272120
082			_a514.74 _bPAT
100			_aPaternain, Gabriel
245			_aGeodesic flows
260			_bSpringer Science, _c1999 _aNew York:
300			_axii, 145p. ; _bpb. ; _c23cm.
365			_aEURO _b74.99
440			_aProgress in Mathematics
504			_aIncludes references and index
520			_aThe aim of this book is to present the fundamental concepts and properties of the geodesic flow of a closed Riemannian manifold. The topics covered are close to my research interests. An important goal here is to describe properties of the geodesic flow which do not require curvature assumptions. A typical example of such a property and a central result in this work is Mane's formula that relates the topological entropy of the geodesic flow with the exponential growth rate of the average numbers of geodesic arcs between two points in the manifold. The material here can be reasonably covered in a one-semester course. I have in mind an audience with prior exposure to the fundamentals of Riemannian geometry and dynamical systems. I am very grateful for the assistance and criticism of several people in preparing the text. In particular, I wish to thank Leonardo Macarini and Nelson Moller who helped me with the writing of the first two chapters and the figures. Gonzalo Tomaria caught several errors and contributed with helpful suggestions. Pablo Spallanzani wrote solutions to several of the exercises. I have used his solutions to write many of the hints and answers. I also wish to thank the referee for a very careful reading of the manuscript and for a large number of comments with corrections and suggestions for improvement
650			_aMathematics
650			_aTopology
650			_aDifferentiable dynamical systems
650			_aGeodesic flows
650			_aManifolds
650			_aDynamics
650			_aProgress in Mathematics, V. 180.
942			_2ddc _cTD