Invitation to Ergodic Theory - Softcover

C.E. Silva

Softcover

ISBN 10: 0821887335 ISBN 13: 9780821887332

Publisher: Orient Black Swan, 2012

Synopsis

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 Caratheodory extension theorem. It also develops the Lebesgue theory of integration, including the dominated convergence theorem and an introduction to the Lebesgue $L^p$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 Chacon 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.

Edition details

• Publisher: Orient Black Swan
• Publication date: 2012
• Language: English
• ISBN 10: 0821887335
• ISBN 13: 9780821887332
• Binding: Paperback
• Number of pages: 262