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101 0 $aeng
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181   $ctxt$2rdacontent
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200 10$aRandomness and recurrence in dynamical systems $ea real analysis approach /$fRodney Nillsen$b[electronic resource]
210  1$aWashington :$cMathematical Association of America,$d2010.
215   $a1 online resource (xviii, 357 pages) $cdigital, PDF file(s)
225 1 $aThe Carus mathematical monographs ;$vno. 31
300   $aTitle from publisher's bibliographic system (viewed on 02 Oct 2015).
311   $a0-88385-043-5 
320   $aIncludes bibliographical references and indexes.
327   $aBackground ideas and knowledge -- Irrational numbers and dynamical systems -- Probability and randomness -- Recurrence -- Averaging in time and space.
330   $aRandomness and Recurrence in Dynamical Systems aims to bridge a gap between undergraduate teaching and the research level in mathematical analysis. It makes ideas on averaging, randomness, and recurrence, which traditionally require measure theory, accessible at the undergraduate and lower graduate level. The author develops new techniques of proof and adapts known proofs to make the material accessible to students with only a background in elementary real analysis.  Over 60 figures are used to explain proofs, provide alternative viewpoints and elaborate on the main text. The book explains further developments in terms of measure theory. The results are presented in the context of dynamical systems, and the quantitative results are related to the underlying qualitative phenomena—chaos, randomness, recurrence and order.   The final part of the book introduces and motivates measure theory and the notion of a measurable set, and describes the relationship of Birkhoff's Individual Ergodic Theorem to the preceding ideas. Developments in other dynamical systems are indicated, in particular Le?vy's result on the frequency of occurence of a given digit in the partial fractions expansion of a number.  Historical notes and comments suggest possible avenues for self-study.
410  0$aCarus mathematical monographs ;$vno. 31.
517 3 $aRandomness & Recurrence in Dynamical Systems
606   $aDifferentiable dynamical systems
606   $aMeasure theory
615  0$aDifferentiable dynamical systems.
615  0$aMeasure theory.
676   $a515.352
700   $aNillsen$b Rodney Victor$f1945-$060688
801  0$bUkCbUP
801  1$bUkCbUP
906   $aBOOK
912   $a9910786846703321
996   $aRandomness and recurrence in dynamical systems$93759342
997   $aUNINA