Randomness and recurrence in dynamical systems : a real analysis approach / / Rodney Nillsen.

• Superior document: The Carus mathematical monographs ; no. 31
• Author: ProQuest (Firm); Nillsen, Rodney Victor, 1945-
• TeilnehmendeR: ProQuest (Firm)
• Year of Publication: 2010
• Language: English
• Series: Carus mathematical monographs ; no. 31.
• Physical Description: xviii, 357 p. :; ill.

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.

Table of Contents

Background ideas and knowledge -- Irrational numbers and dynamical systems -- Probability and randomness -- Recurrence -- Averaging in time and space.