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By Gabriel P. Paternain

the purpose of this e-book is to offer the elemental options and houses of the geodesic circulation of a closed Riemannian manifold. the themes lined are with reference to my examine pursuits. a huge aim here's to explain houses of the geodesic stream which don't require curvature assumptions. a standard instance of this kind of estate and a significant lead to this paintings is Mane's formulation that relates the topological entropy of the geodesic circulate with the exponential development cost of the common numbers of geodesic arcs among issues within the manifold. the fabric right here should be kind of lined in a one-semester path. i've got in brain an viewers with earlier publicity to the basics of Riemannian geometry and dynamical platforms. i'm very thankful for the help and feedback of a number of humans in getting ready the textual content. specifically, I desire to thank Leonardo Macarini and Nelson Moller who helped me with the writing of the 1st chapters and the figures. Gonzalo Tomaria stuck numerous error and contributed with precious feedback. Pablo Spallanzani wrote recommendations to a number of of the workouts. i've got used his suggestions to jot down a few of the tricks and solutions. I additionally desire to thank the referee for a truly cautious studying of the manuscript and for various reviews with corrections and recommendations for improvement.

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Geodesic Flows (Progress in Mathematics) by Gabriel P. Paternain

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