02507nam a2200385Ii 4500991003575059707536m o d cr cnu|||unuuu181122s2017 sz a o 000 0 eng d9783319430591(electronic bk.)3319430599(electronic bk.)10.1007/978-3-319-43059-1doib14354020-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.4823AMS 37-06LC QA313Ergodic Theory and Negative Curvature[e-book] :CIRM Jean-Morlet Chair, Fall 2013 /edited by Boris HasselblattCham, Switzerland :Springer,20171 online resource (vii, 328 pages) :illustrations (some color)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture notes in mathematics,0075-8434 ;2164Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research. It offers original textbook-level material suitable for introductory or advanced courses as well as deep insights into the state of the art of the field, making it useful as a reference and for self-study.  The first chapters introduce hyperbolic dynamics, ergodic theory and geodesic and horocycle flows, and include an English translation of Hadamard's original proof of the Stable-Manifold Theorem. An outline of the strategy, motivation and context behind the ergodicity proof is followed by a careful exposition of it (using the Hopf argument) and of the pertinent context of Teichmüller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximationErgodic theoryCongressesDynamicsHasselblatt, BorisPrinted edition:9783319430584https://link.springer.com/book/10.1007/978-3-319-43059-1An electronic book accessible through the World Wide.b1435402003-03-2222-11-18991003575059707536Ergodic theory and negative curvature1522941UNISALENTOle01322-11-18m@ -engsz 00