Randomness and recurrence in dynamical systems : a real analysis approach / / Rodney Nillsen [[electronic resource]]

• Autore: Nillsen Rodney Victor <1945->
• Pubblicazione: Washington : , : Mathematical Association of America, , 2010
• Descrizione fisica: 1 online resource (xviii, 357 pages) : digital, PDF file(s)
• Disciplina: 515.352
• Soggetto topico: Differentiable dynamical systems; Measure theory
• Note generali: Title from publisher's bibliographic system (viewed on 02 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: Background ideas and knowledge -- Irrational numbers and dynamical systems -- Probability and randomness -- Recurrence -- Averaging in time and space.
• Sommario/riassunto: 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 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 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 self-study.
• Altri titoli varianti: Randomness & Recurrence in Dynamical Systems
• Titolo autorizzato: Randomness and recurrence in dynamical systems
• ISBN: 1-61444-000-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910821848903321
• Lo trovi qui: Univ. Federico II
• Serie: Carus mathematical monographs ; ; no. 31.