Randomness and recurrence in dynamical systems
Subtitle: a real analysis approach
By: Rodney Nillsen
Series: The Carus mathematical monographs -- no. 31; Carus mathematical monographs -- no. 31.
Publisher: Mathematical Association of America
Published: 2010
Place of publication: Washington, DC
Language: eng
Number of pages: 357
ISBN-13: 9780883850435
Subjects: Measure theory; Differentiable dynamical systems
Description: 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.--
Notes: Includes bibliographical references and indexes.
Table of contents: title: Background ideas and knowledge; title: Irrational numbers and dynamical systems; title: Probability and randomness; title: Recurrence; title: Averaging in time and space.