Fundamentals Of Measurable Dynamics
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Fundamentals of Measurable Dynamics
Author: Daniel J. Rudolph
language: en
Publisher: Oxford University Press, USA
Release Date: 1990
This book is designed to provide graduate students and other researchers in dynamical systems theory with an introduction to the ergodic theory of Lebesgue spaces. The author's aim is to present a technically complete account which offers an in-depth understanding of the techniques of the field, both classical and modern. Thus, the basic structure theorems of Lebesgue spaces are given in detail as well as complete accounts of the ergodic theory of a single transformation, ergodic theorems, mixing properties and entropy. Subsequent chapters extend the earlier material to the areas of joinings and representation theorems, in particular the theorems of Ornstein and Krieger. Prerequisites are a working knowledge of Lebesgue measure and the topology of the real line as might be gained from the first year of a graduate course. Many exercises and examples are included to illustrate and to further cement the reader's understanding of the material. The result is a text which will furnish the reader with a sound technical background from the foundations of the subject to some of its most recent developments.
Dynamical Systems and Ergodic Theory
Author: Mark Pollicott
language: en
Publisher: Cambridge University Press
Release Date: 1998-01-29
This book is an essentially self contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a masters level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der waerden's theorem and szemerdi's theorem).
An Introduction to Symbolic Dynamics and Coding
Author: Douglas A. Lind
language: en
Publisher: Cambridge University Press
Release Date: 2021-01-21
Elementary introduction to symbolic dynamics, updated to describe the main advances in the subject since the original publication in 1995.