RANDOMNESS AND RECURRENCE IN DYNAMICAL SYSTEMS
RANDOMNESS AND RECURRENCE IN DYNAMICAL SYSTEMS
 Item No.
 CAM31
 Price:
 $62.95
Product Details
Randomness and Recurrence in Dynamical Systems
by Rodney Nillsen
The book is very well written and the author clearly motivates all definitions and theorems. MAA Reviews
Randomness 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 phenomenachaos, 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 Lévy'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 selfstudy.
 Brand name: MAA
 Author: Rodney Nillsen
 ISBN:9780883850435
 357 pp.
 Hardcover
 2010
 Series: Carus Mathematical Monograph
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