02594nam a2200361 a 4500 ebr10722467 CaPaEBR m o u cr cn||||||||| 100318s2010 dcua sb 001 0 eng d 2010924993 0883850435 9780883850435 9781614440000 (e-book) CaPaEBR CaPaEBR (OCoLC)817962637 QA614.8 .N55 2010eb Nillsen, Rodney Victor, 1945- Randomness and recurrence in dynamical systems [electronic resource] : a real analysis approach / Rodney Nillsen. Washington, D.C. : Mathematical Association of America, c2010. xviii, 357 p. : ill. The Carus mathematical monographs ; no. 31 Includes bibliographical references and indexes. Background ideas and knowledge -- Irrational numbers and dynamical systems -- Probability and randomness -- Recurrence -- Averaging in time and space. Randomness 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-- Source other than Library of Congress. Electronic reproduction. Palo Alto, Calif. : ebrary, 2013. Available via World Wide Web. Access may be limited to ebrary affiliated libraries. Differentiable dynamical systems. Measure theory. Electronic books. local ebrary, Inc. Carus mathematical monographs ; no. 31. http://site.ebrary.com/lib/rucke/Doc?id=10722467 An electronic book accessible through the World Wide Web; click to view 39384 39384