Invitation to ergodic theory
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Item type | Current library | Call number | Status | Date due | Barcode |
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NISER LIBRARY | 519.218.84 SIL-I (Browse shelf(Opens below)) | Available | N112 | |
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SMS Library | 519.218.84 SIL-I (Browse shelf(Opens below)) | Available | N426 |
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519.218.84 NAD-B Basic ergodic theory | 519.218.84 NAD-B Basic ergodic theory | 519.218.84 SAH-N Non-commutative neveu decomposition and associated ergodic theorems | 519.218.84 SIL-I Invitation to ergodic theory | 519.218.84 VIA-F Foundations of ergodic theory | 519.219 BOV-R Random walks, random fields, and disordered systems | 519.219 DAM-M The mathematics of signal processing |
Includes bibliographical references and index.
This book is an introduction to basic concepts in ergodic theory such as recurrence, ergodicity, the ergodic theorem, mixing, and weak mixing. It does not assume knowledge of measure theory; all the results needed from measure theory are presented from scratch. In particular, the book includes a detailed construction of the Lebesgue measure on the real line and an introduction to measure spaces up to the Carathéodory extension theorem. It also develops the Lebesgue theory of integration, including the dominated convergence theorem and an introduction to the Lebesgue Lp
spaces.
Several examples of a dynamical system are developed in detail to illustrate various dynamical concepts. These include in particular the baker's transformation, irrational rotations, the dyadic odometer, the Hajian–Kakutani transformation, the Gauss transformation, and the Chacón transformation. There is a detailed discussion of cutting and stacking transformations in ergodic theory. The book includes several exercises and some open questions to give the flavor of current research. The book also introduces some notions from topological dynamics, such as minimality, transitivity and symbolic spaces; and develops some metric topology, including the Baire category theorem.
Undergraduate and graduate students interested in ergodic theory and measure theory.
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