03073nam a22004815i 4500 978-0-85729-021-2 DE-He213 20260521092035.0 cr nn 008mamaa 100917s2011 xxk| s |||| 0|eng d 9780857290212 99780857290212 10.1007/978-0-85729-021-2 doi 515.39 23 515.48 23 Einsiedler, Manfred. author. Ergodic Theory [electronic resource] : with a view towards Number Theory / by Manfred Einsiedler, Thomas Ward. London : Springer London, 2011. XVIII, 482 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Graduate Texts in Mathematics, 0072-5285 ; 259 Motivation -- 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. This 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. MATHEMATICS. DIFFERENTIABLE DYNAMICAL SYSTEMS. NUMBER THEORY. MATHEMATICS. DYNAMICAL SYSTEMS AND ERGODIC THEORY. NUMBER THEORY. MEASURE AND INTEGRATION. Ward, Thomas. author. SpringerLink (Online service) Springer eBooks Printed edition: 9780857290205 Graduate Texts in Mathematics, 0072-5285 ; 259 http://dx.doi.org/10.1007/978-0-85729-021-2 Ver el texto completo en las instalaciones del CICY ZDB-2-SMA ddc ER 35852 35852 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 515.39 | 515.48 2025-10-06 08:44:41 2025-10-06 ER