LEADER 03386nam 2200493 450 001 9910736006603321 005 20231020211222.0 010 $a1-0716-2388-5 024 7 $a10.1007/978-1-0716-2388-6 035 $a(CKB)5580000000567220 035 $a(DE-He213)978-1-0716-2388-6 035 $a(MiAaPQ)EBC30766656 035 $a(Au-PeEL)EBL30766656 035 $a(PPN)272253782 035 $a(EXLCZ)995580000000567220 100 $a20231020d2023 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aErgodic Theory /$fCesar E. Silva and Alexandre I. Danilenko, editors 205 $aFirst edition. 210 1$aNew York, NY :$cSpringer Science+Business Media, LLC,$d[2023] 210 4$dİ2023 215 $a1 online resource (50 illus., 35 illus. in color. eReference.) 225 1 $aEncyclopedia of Complexity and Systems Science Series 311 $a1-0716-2387-7 320 $aIncludes bibliographical references and index. 327 $aIntroduction to Ergodic Theory -- Ergodic Theory: Basic Examples and Constructions -- Ergodicity and Mixing Properties -- Ergodic Theory: Recurrence -- Ergodic Theorems -- Spectral Theory of Dynamical Systems -- Joinings in Ergodic Theory -- Entropy in Ergodic Theory -- Isomorphism Theory in Ergodic Theory -- Dynamical Systems of Probabilistic Origin: Gaussian and Poisson Systems -- Ergodic Theory: Non-singular Transformations -- Sarnak?s Conjecture from the Ergodic Theory Point of View -- Smooth Ergodic Theory -- Ergodic and spectral theory of area-preserving flows on surfaces -- Pressure and Equilibrium States in Ergodic Theory -- Parallels Between Topological Dynamics and Ergodic Theory -- Symbolic Dynamics -- Operator ergodic theory -- Dynamical Systems and C-algebras -- The complexity and the structure and classification of Dynamical Systems -- Ergodic Theory: Interactions with Combinatorics and Number Theory -- Ergodic Theory on Homogeneous Spaces and Metric Number Theory -- Ergodic Theory: Rigidity -- Chaos and Ergodic Theory -- Ergodic Theory: Fractal Geometry. 330 $aThis volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras. 410 0$aEncyclopedia of complexity and systems science series. 606 $aErgodic theory 615 0$aErgodic theory. 676 $a515.42 702 $aSilva$b Cesar E. 702 $aDanilenko$b Alexandre I. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910736006603321 996 $aErgodic theory$980545 997 $aUNINA