02934nam a22004335i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024003500137082001500172082001500187100003400202245011800236264003800354300003600392336002600428337002600454338003600480347002400516490005300540505048400593520097101077650001702048650003802065650001902103650001702122650004202139650001902181650002902200700002702229710003402256773002002290776003602310830005302346856010102399978-0-85729-021-2DE-He21320260521092035.0cr nn 008mamaa100917s2011    xxk|    s    |||| 0|eng d  a9780857290212  a997808572902127 a10.1007/978-0-85729-021-22doi04a515.3922304a515.482231 aEinsiedler, Manfred.eauthor.10aErgodic Theoryh[electronic resource] :bwith a view towards Number Theory /cby Manfred Einsiedler, Thomas Ward. 1aLondon :bSpringer London,c2011.  aXVIII, 482 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aGraduate Texts in Mathematics,x0072-5285 ;v2590 aMotivation -- Ergodicity, Recurrence and Mixing -- Continued Fractions -- Invariant Measures for Continuous Maps -- Conditional Measures and Algebras -- Factors and Joinings -- Furstenberg's Proof of Szemeredi's Theorem -- Actions of Locally Compact Groups -- Geodesic Flow on Quotients of the Hyperbolic Plane -- Nilrotation -- More Dynamics on Quotients of the Hyperbolic Plane -- Appendix A: Measure Theory -- Appendix B: Functional Analysis -- Appendix C: Topological Groups.  aThis text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory. 0aMATHEMATICS. 0aDIFFERENTIABLE DYNAMICAL SYSTEMS. 0aNUMBER THEORY.14aMATHEMATICS.24aDYNAMICAL SYSTEMS AND ERGODIC THEORY.24aNUMBER THEORY.24aMEASURE AND INTEGRATION.1 aWard, Thomas.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780857290205 0aGraduate Texts in Mathematics,x0072-5285 ;v25940uhttp://dx.doi.org/10.1007/978-0-85729-021-2zVer el texto completo en las instalaciones del CICY