03508nam 22005295i 4500001001800000003000900018005001700027007001500044008004100059020003700100024002500137040002500162050001000187072001700197072002300214072001600237082001500253082001500268100007600283245007600359264006100435300004400496336002600540337002600566338003600592347002400628490006400652505039900716520102701115650003802142650002902180650011302209650012802322650011902450710003402569773002002603776003602623776003602659776003602695830006402731856003602795912001402831942000702845950004802852999001902900952005902919978-3-540-27305-9DE-He21320181203160144.0cr nn 008mamaa100301s2005 gw | s |||| 0|eng d a97835402730599978-3-540-27305-97 a10.1007/b1388942doi aISI Library, Kolkata 4aQA313 7aPBWR2bicssc 7aMAT0340002bisacsh 7aPBWR2thema04a515.3922304a515.482231 aChoe, Geon Ho.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aComputational Ergodic Theoryh[electronic resource] /cby Geon Ho Choe. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg,c2005. aXX, 453 p. 250 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aAlgorithms and Computation in Mathematics,x1431-1550 ;v130 aPrerequisites -- Invariant Measures -- The Birkhoff Ergodic Theorem -- The Central Limit Theorem -- More on Ergodicity -- Homeomorphisms of the Circle -- Mod 2 Uniform Distribution -- Entropy -- The Lyapunov Exponent: One-Dimensional Case -- The Lyapunov Exponent: Multidimensional Case -- Stable and Unstable Manifolds -- Recurrence and Entropy -- Recurrence and Dimension -- Data Compression. aErgodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. Many of the examples are introduced from a different perspective than in other books and theoretical ideas can be gradually absorbed while doing computer experiments. Theoretically less prepared students can appreciate the deep theorems by doing various simulations. The computer experiments are simple but they have close ties with theoretical implications. Even the researchers in the field can benefit by checking their conjectures, which might have been regarded as unrealistic to be programmed easily, against numerical output using some of the ideas in the book. One last remark: The last chapter explains the relation between entropy and data compression, which belongs to information theory and not to ergodic theory. It will help students to gain an understanding of the digital technology that has shaped the modern information society. 0aDifferentiable dynamical systems. 0aEngineering mathematics.14aDynamical Systems and Ergodic Theory.0http://scigraph.springernature.com/things/product-market-codes/M1204X24aTheoretical, Mathematical and Computational Physics.0http://scigraph.springernature.com/things/product-market-codes/P1900524aMathematical and Computational Engineering.0http://scigraph.springernature.com/things/product-market-codes/T110062 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978354080396608iPrinted edition:z978364206207008iPrinted edition:z9783540231219 0aAlgorithms and Computation in Mathematics,x1431-1550 ;v1340uhttps://doi.org/10.1007/b138894 aZDB-2-SMA cEB aMathematics and Statistics (Springer-11649) c424990d424990 9275579aMAINbMAINd2017-04-01pEB1131r2018-12-03yEB