02594nam a2200361 a 4500001001200000003000800012006001900020007001500039008004100054010001700095020001500112020001800127020002700145040002100172035002100193050002500214100003500239245012100274260006900395300002600464490004800490504005300538505015500591520104200746533015201788650003801940650002001978655002901998710001702027830004502044856012602089999001702215ebr10722467CaPaEBRm     o  u        cr cn|||||||||100318s2010    dcua    sb    001 0 eng d  z  2010924993  z0883850435  z9780883850435  z9781614440000 (e-book)  aCaPaEBRcCaPaEBR  a(OCoLC)81796263714aQA614.8b.N55 2010eb1 aNillsen, Rodney Victor,d1945-10aRandomness and recurrence in dynamical systemsh[electronic resource] :ba real analysis approach /cRodney Nillsen.  aWashington, D.C. :bMathematical Association of America,cc2010.  axviii, 357 p. :bill.1 aThe Carus mathematical monographs ;vno. 31  aIncludes bibliographical references and indexes.0 aBackground ideas and knowledge -- Irrational numbers and dynamical systems -- Probability and randomness -- Recurrence -- Averaging in time and space.  aRandomness and Recurrence in Dynamical Systems makes accessible, at the undergraduate or beginning graduate level, results and ideas on averaging, randomness and recurrence that traditionally require measure theory. Assuming only a background in elementary calculus and real analysis, new techniques of proof have been developed, and known proofs have been adapted, to make this possible. The book connects the material with recent research, thereby bridging the gap between undergraduate teaching and current mathematical research. The various topics are unified by the concept of an abstract dynamical system, so there are close connections with what may be termed 'Probabilistic Chaos Theory' or 'Randomness'. The work is appropriate for undergraduate courses in real analysis, dynamical systems, random and chaotic phenomena and probability. It will also be suitable for readers who are interested in mathematical ideas of randomness and recurrence, but who have no measure theory background--cSource other than Library of Congress.  aElectronic reproduction.bPalo Alto, Calif. :cebrary,d2013.nAvailable via World Wide Web.nAccess may be limited to ebrary affiliated libraries. 0aDifferentiable dynamical systems. 0aMeasure theory. 7aElectronic books.2local2 aebrary, Inc. 0aCarus mathematical monographs ;vno. 31.40uhttp://site.ebrary.com/lib/rucke/Doc?id=10722467zAn electronic book accessible through the World Wide Web; click to view  c39384d39384