LEADER 02507nam a2200385Ii 4500 001 991003575059707536 006 m o d 007 cr cnu|||unuuu 008 181122s2017 sz a o 000 0 eng d 020 $a9783319430591$q(electronic bk.) 020 $a3319430599$q(electronic bk.) 024 7 $a10.1007/978-3-319-43059-1$2doi 035 $ab14354020-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a515.48$223 084 $aAMS 37-06 084 $aLC QA313 245 00$aErgodic Theory and Negative Curvature$h[e-book] :$bCIRM Jean-Morlet Chair, Fall 2013 /$cedited by Boris Hasselblatt 264 1$aCham, Switzerland :$bSpringer,$c2017 300 $a1 online resource (vii, 328 pages) :$billustrations (some color) 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2164 520 $aFocussing on the mathematics related to the recent proof of ergodicity of the (Weil?Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research. It offers original textbook-level material suitable for introductory or advanced courses as well as deep insights into the state of the art of the field, making it useful as a reference and for self-study.  The first chapters introduce hyperbolic dynamics, ergodic theory and geodesic and horocycle flows, and include an English translation of Hadamard's original proof of the Stable-Manifold Theorem. An outline of the strategy, motivation and context behind the ergodicity proof is followed by a careful exposition of it (using the Hopf argument) and of the pertinent context of Teichmüller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximation 650 0$aErgodic theory$vCongresses 650 0$aDynamics 700 1 $aHasselblatt, Boris 776 08$iPrinted edition:$z9783319430584 856 40$uhttps://link.springer.com/book/10.1007/978-3-319-43059-1$zAn electronic book accessible through the World Wide 907 $a.b14354020$b03-03-22$c22-11-18 912 $a991003575059707536 996 $aErgodic theory and negative curvature$91522941 997 $aUNISALENTO 998 $ale013$b22-11-18$cm$d@ $e-$feng$gsz $h0$i0